Lattice gauge theory

This work proposes a mechanical foundation beneath General Relativity and Quantum Mechanics: a wave-based model in which spacetime is a tensioned medium. While Einstein described how mass curves spacetime, this framework investigates what physically curves — suggesting that curvature arises from mechanical strain in an oscillating substructure. Where quantum mechanics deals with probabilities, this theory derives them from constraints in a real, vibrating substrate — the very fabric of space. This is the unifying mechanical model Einstein sought — a testable, mathematically consistent theory combining gravity, quantum mechanics, and cosmology. The medium obeys relativistic wave equations and exhibits no preferred frame, ensuring compatibility with Lorentz invariance. Ultronic Medium Hypothesis (UMH) reproduces the frequency evolution, chirp mass behavior, and strain amplitudes of gravitational waves detected by LIGO. It simulates a CMB angular power spectrum matching observed acoustic peaks, without invoking inflation or metric expansion. UMH derives the Hubble relation as a result of tension evolution in the medium, not expanding space. It shows that the Einstein tensor converges to zero in vacuum, recovering GR from strain curvature instead of abstract manifolds. UMH treats GR and QFT as continuum and statistical approximations of an underlying Planck-scale wave medium — the Ultronic Medium. This tensioned lattice yields spacetime curvature macroscopically and solitonic, phase-locked oscillations microscopically, explaining quantum statistics, fermions, and decoherence. Simulations match CMB data, redshift relations, and LIGO strains. The model eliminates dark energy, dark matter, and the cosmological constant via reinterpretation of large-scale strain curvature. Coupling constants emerge as topological strain energies, matching experimental values within 10%.

The Source Energy Field Theory (SEFT) extends the freedom to define spacetime itself as a manifestation of the fundamental energy field. This enhanced degree of freedom allows the Standard Model gauge symmetries and the Higgs mechanism to emerge as natural geometric consequences, rather than imposed assumptions. While its application to cosmology has successfully explained supernova redshiftdistance relations, galactic rotation curves, and the cosmic microwave background, its implications for particle physics have remained unexplored. In this paper, we extend SEFT to the domain of particle physics and demonstrate that and preserving the custodial relation ρ = 1. These results establish SEFT as a framework in which the core architecture of the Standard Model is embedded in the dynamics of a single fundamental field, thus providing the particle-physics counterpart to the cosmological results previously derived in SEFT.

The set-up of the QCD Schrödinger functional (SF) on the lattice with staggered quarks requires an even number of points L/a in the spatial directions, while the Euclidean time extent of the lattice, T /a, must be odd. Identifying a unique renormalisation scale, L = T , is then only possible up to O(a) lattice artefacts. In this article we study such lattices in the pure SU(3) gauge theory, where we can also compare to the standard set-up. We consider the SF coupling as obtained from the variation of an SU(3) Abelian and spatially constant background field. The O(a) lattice artefacts can be cancelled by the existing O(a) boundary counterterm. However, its coefficient, c t , differs at the tree-level from its standard value, so that one first needs to re-determine the induced background gauge field. The perturbative one-loop correction to the coupling allows to determine c t to one-loop order. A few numerical simulations serve to demonstrate that residual cutoff effects in the step scaling function are small in both cases, T = L ± a and comparable to the standard case with T = L. 1 For staggered quarks we here use the traditional term "flavour" rather than "taste".

We introduce Chronon Field Theory (CFT) as a minimal and self-consistent framework in which conventional spacetime geometry and gauge interactions emerge from a single dynamical temporal field, eliminating the need for a fundamental spacetime manifold. Specifically, a smooth, unit-norm, future-directed timelike vector field Φ µ (x) generates local causal structure, effective spacetime geometry, and emergent gauge interactions without reliance on a background metric or fundamental gauge bosons. The theory yields Einstein-like gravitational dynamics, with the effective metric and connection derived from the foliation induced by Φ µ. A local U (1) symmetry arises from internal phase rotations, giving rise to Maxwell electrodynamics in the weak-field limit, with the photon appearing as a Goldstone-like excitation. We derive explicit field equations, demonstrate local energy conservation from Noether currents, and identify vacuum birefringence as a concrete observational signature potentially accessible to forthcoming CMB polarization experiments. If confirmed, we suggest that CFT could support practical technologies currently limited by relativistic time ambiguity-such as a globally synchronized, GPS-independent positioning and communication network based on direct coupling to the underlying temporal field. CFT thereby provides a unified and empirically accessible alternative to standard geometric and gauge-theoretic foundations of fundamental physics.

We ask how Lorentzian causal structure can emerge from a pregeometric substrate. For a rigorously defined class of finite-range, ferromagnetically coupled "chronon" models with quartic norm pinning, we prove the existence, with strictly positive Gibbs probability, of a macroscopic percolating domain 𝐷 ⊂ 𝑀 on which the coarse-grained field Φ 𝜇 is smooth, future-directed, unit-norm timelike (Φ 𝜇 Φ 𝜇 =-1, Φ 0 > 0) and twist-free. We work on a smooth differentiable manifold but do not assume Lorentzian signature or a global time field a priori; these arise on 𝐷 from the dynamics. Under four operational axioms-well-posed local dynamics, finite-speed signalling, acyclic causal order, and stable memory/records-we further prove that no alternative (Euclidean or ultrahyperbolic) signature, nor a Lorentzian background lacking a globally unit-norm time field, can sustain such behavior; the Lorentzian, unit-norm phase is therefore exclusive. Finally, we show that "measurement" acts as a boundary-induced selector of this phase: an interface coupling to an aligned apparatus field Φ 𝐴 admits a unique minimizer, pins the norm and alignment, suppresses twist, and drives any initial state to the aligned phase with exponential convergence; largedeviation bounds quantify high-fidelity selection. While our theorems hold for general (1, 𝑑) signatures with 𝑑 ≥ 1, heuristic coarse-graining and stability considerations suggest 𝑑 = 3 as the most probable large-scale outcome. Together, these results provide a mathematically controlled foundation for the emergence and exclusivity of Lorentzian causal structure and for boundary-driven selection (measurement) in pregeometric ensembles.

We present Chronon Field Theory (CFT), a covariant framework in which large-scale spacetime geometry-including temporal order and causal structure-emerges from the coarse-grained dynamics of a single future-directed timelike field Φ µ (x). Within this approach, both the unit-norm property of Φ µ and the Lorentzian signature of g µν are not postulated but arise uniquely from random microscopic chronon dynamics under broad symmetry and locality assumptions. Quantum phenomena are reinterpreted in this geometric setting: double-slit interference results from phase-coherent Φ-threads rather than superposed particle paths, and measurement appears as a boundary-induced alignment of microscopic orientations with the apparatus's macroscopic field, yielding definite outcomes without collapse or branching. Schrödinger's cat is then a straightforward macro-micro coupling with no persistent macroscopic superposition, while EPR-type entanglement reflects shared Φ-thread ancestry across spacelike separations. The Born rule follows from the unbiased martingale structure of alignment dynamics and from coarse-graining symmetries, making it an emergent statistical law; the uncertainty principle appears as a statistical bound on chronon fluctuations, with h arising as the variance of coarse-grained action. CFT thus provides a covariant and ontologically economical framework linking spacetime symmetries to quantum measurement, and predicts scale-dependent effects-such as nonlinear decoherence and curvature-sensitive timing shifts-that are open to experimental test.

We present a self-contained formulation of Chronon Field Theory (CFT) in which (i) a smooth, unit-norm, future-directed timelike field Φ µ induces foliation, causal structure, and an emergent Lorentzian metric; (ii) a covariant local mass/energy density is defined as ρ(x) = T µν Φ µ Φ µ , furnishing a unified and positive notion of inertial/gravitational mass; (iii) matter arises as topologically stable solitons with w = 1, carrying spin-1 2 and Fermi-Dirac statistics via a Finkelstein-Rubinstein/Berry holonomy mechanism; and (iv) a U(1) gauge sector emerges from chronon holonomy, yielding Maxwell dynamics on the emergent metric and a massless "photon" as a Goldstone-like excitation. We prove positivity and conservation properties for ρ, establish existence of finite-energy soliton minimizers under mild assumptions, and state a holonomy-matching theorem that ties the FR Z 2 class to the emergent spacetime U(1) connection. A key outcome is that the familiar constants of Nature are not postulated but emerge: the effective action unit ℏ eff ∼ E c τ c , Newton's constant G ∼ (c(α i , γ)Λ 2)-1 , the elementary charge e = q 0 / √ κ A , and the universal light speed c = ℓ Φ /τ c. In the gravitational sector we recover Einstein-Maxwell on stabilized domains at two-derivative order, while allowing controlled, power-counted deviations (aether-like and higher-derivative terms) that are constrained phenomenologically. We further derive the Coulomb law on stabilized leaves, V (r) = e 1 e 2 /(4πr), whose normalization fixes the holonomy stiffness via the observed Coulomb constant (equivalently α em), yielding κ A = q 2 0 /(4πα em). We outline collective-coordinate quantization where splittings scale with ℏ eff , and identify falsifiable signatures (achromatic birefringence; exchange-phase interferometry). This paper (I) lays the foundation for non-Abelian extensions (II) and QCD-like dynamics (III).

We extend Chronon Field Theory (CFT) beyond the emergent U(1) sector by constructing a compact non-Abelian holonomy from the internal geometry of the chronon field Φ µ. We prove existence of an emergent principal SU(2) bundle and connection, derive the Yang-Mills action on the emergent metric g µν [Φ], and show how vector boson masses arise without a fundamental scalar: either via a Stückelberg-like realization of internal phases or through a composite amplitude mode of Φ. We demonstrate that a residual U(1) combination remains unbroken, ensuring an exactly massless photon as in QED, and we establish Ward/Slavnov-Taylor identities and tree-level unitarity for longitudinal vector scattering. Solitonic matter from Paper I is minimally coupled through the emergent connection; we extract phenomenological constraints from precision electroweak data and outline a path to SU(3) (Paper III).

We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. Such actions originate from the admissibility condition in order to conserve the topological charge. The suppression of small plaquette values is expected to be advantageous for numerical studies in the ε-regime and also for simulations with dynamical quarks. Performing simulations at a lattice spacing of about 0.1 fm, we present numerical results for the static potential, the physical scale r 0 , the stability of the topological charge history, the condition number of the kernel of the overlap operator and the acceptance rate against the step size in the local HMC algorithm.

We explore gauge actions for lattice QCD, which are constructed such that the occurrence of small plaquette values is strongly suppressed. By choosing strong bare gauge couplings we arrive at values for the physical lattice spacings of O(0.1 fm). Such gauge actions tend to confine the Monte Carlo history to a single topological sector. This topological stability facilitates the collection of a large set of configurations in a specific sector, which is profitable for numerical studies in the ǫ-regime. The suppression of small plaquette values is also expected to be favourable for simulations with dynamical quarks. We use a local Hybrid Monte Carlo algorithm to simulate such actions, and we present numerical results for the static potential, the physical scale, the topological stability and the kernel condition number of the overlap Dirac operator. In addition we discuss the question of reflection positivity for a class of such gauge actions.

Zusammenfassung Die RMB-Theorie (Raum-Materie-Bewegung) wird in RMB V um die vollständigen mathematischen Herleitungen der in RMB IV definierten fraktalen Resonanzkorrekturen und Feldkoppelungen erweitert. Besonderes Augenmerk liegt auf der exakten Dimensionsanalyse der Kopplungskonstanten α RMB , β RMB , κ RMB , der Dynamik des Bewegungstensors M µν sowie der Implementierung der fraktalen Fourier-Korrekturen nach Cairo (2025). Darüber hinaus wird ein konsistenter Hamilton-und Pfadintegralformalismus entwickelt, um die Quantisierung durch Gravonons im Kontext des Standardmodells zu ermöglichen. Experimentelle Vorhersagen für Casimir-Effekte, Flyby-Anomalien und 21 cm-Linien werden konsistent hergeleitet. RMB V bildet damit die notwendige Brücke von RMB IV zur vollständigen empirischen Validierung.

We review recent results from studies of the dynamics of classical Yang-Mills fields on a lattice. We discuss the numerical techniques employed in solving the classical lattice Yang-Mills equations in real time, and present results exhibiting the universal chaotic behavior of nonabelian gauge theories. The complete spectrum of Lyapunov exponents is determined for the gauge group SU(2). We survey results obtained for the SU(3) gauge theory and other nonlinear field theories. We also discuss the relevance of these results to the problem of thermalization in gauge theories.

We determine numerically the full complex Lyapunov spectrum of SU(2) Yang-Mills fields on a 3-dimensional lattice from the classical chaotic dynamics using eigenvalues of the monodromy matrix. The microcanonical equation of state is determined as the entropy -energy relation utilizing the Kolmogorov-Sinai entropy extrapolated to the large size limit.

Comparison with the Standard Model. It is important to emphasize how the U(3) ZPE scalar field theory approach differs from the Standard Model (SM) in its treatment of divergences. The SM achieves its extraordinary precision through the machinery of renormalization: bare parameters are redefined order by order so that infinities cancel and finite, measurable predictions remain. While this technique is mathematically consistent and empirically spectacular, it leaves open the question of fundamentality: the underlying bare quantities have no physical meaning, and the theory does not explain why the observed parameters (Yukawa couplings, mixing angles, the cosmological constant) take their particular values. By contrast, in the U(3) condensate framework there is a physical ultraviolet cutoff set by the coherence length of the vacuum. Loop integrals are finite by construction, because the field ceases to behave as pointlike beyond this scale. This eliminates the need for renormalization as a mathematical trick, replacing it with a concrete physical regularization rooted in the microstructure of the vacuum. Moreover, the parameters of the low-energy theory-fermion masses, mixing matrices, and coupling strengths-are not arbitrary inputs but emergent quantities derived from the condensate dynamics. In this sense, the theory is not merely an effective description but aspires to be a fundamental account of why the Standard Model takes the form it does. 0.1 Comparison with Other Approaches to Unification It is useful to situate the U(3) condensate framework in the broader landscape of unification programs. Several major approaches have been pursued over the past decades, each with notable strengths but also limitations that our model addresses in a novel way. String Theory. String theory aspires to a complete quantum gravity, embedding all particles as string excitations in higher-dimensional space-times. Its mathematical structure is elegant and has yielded powerful tools (e.g. AdS/CFT),

We construct the Euclidean Yang–Mills theory with gauge group SU(3) on R⁴ as a continuum limit of an RP-preserving lattice regularization. Within the RP/OS/KP framework we establish: (1) existence of a mass gap with a constructive lower bound; (2) restoration of O(4) symmetry in the continuum limit; (3) commutativity of limits for lattice spacing and volume; (4) uniqueness of the vacuum state; (5) non-Gaussianity of the limiting measure. The approach avoids weak-coupling assumptions and relies instead on an RP-compatible odd channel, polymer expansion, and constructive estimates. All constants are uniform in volume, and the analysis is carried out at a fixed physical scale inside the KP window.

We present a strengthened candidate proof for the Yang-Mills mass gap in 4dimensional SU(N) gauge theory. By integrating lattice simulations, two-point correlators, effective mass analysis, continuum extrapolation, constructive renormalization group (RG) arguments, cluster expansions, topological control, and analytic lower bounds, we establish a quantitative lower bound m 0 ≈ 0.395 > 0 for the mass gap in the continuum limit. All numerical, analytical, and RG components are cross-validated. Reproducible code and LaTeX sources are provided for peer review.

We propose a lattice version of Chern-Simons gravity and show that the partition function coincides with Ponzano-Regge model and the action leads to the Chern-Simons gravity in the continuum limit. The action is explicitly constructed by lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformation and gauge diffeomorphism. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.

Earlier investigations [1] showed local minima in the monopole-antimonopole potential in U(1) gauge theory on the lattice. In this paper we localize monopoles of Monte-Carlo configurations. A statistical analysis of localization measurements gives us the probability density which we compare with the potential found in [1]. We find the monopoles mainly located either in the center of three-dimensional cubes or on the interface between two cubes. This agrees with the position of minima and maxima of the monopole-antimonopole potential.

Abelian gauge theories formulated on a space-time lattice can be used as a prototype for investigating the confinement mechanism. In U (1) lattice gauge theory it is possible to perform a dual transformation of the path integral. Simulating the obtained dual theory (which corresponds to a certain limit of a dual Higgs model) including external sources, we perform a very accurate analysis of flux tubes with respect to the dual superconductor picture. Dual flux tube simulations are also performed in the full Abelian Higgs model, in order to obtain non-perturbative control over quantum and string fluctuations, and for a comparison to the results of dual QCD.

Starting from the strong-coupling SU(2) Wilson action in D = 3 dimensions, we derive an effective, semi-local action on a lattice of spacing L times the spacing of the original lattice. It is shown that beyond the adjoint color-screening distance, i.e. for L ≥ 5, thin center vortices are stable saddlepoints of the corresponding effective action. Since the entropy of these stable objects exceeds their energy, center vortices percolate throughout the lattice, and confine color charge in half-integer representations of the SU(2) gauge group. This result contradicts the folklore that confinement in strong-coupling lattice gauge theory, for D > 2 dimensions, is simply due to plaquette disorder, as is the case in D = 2 dimensions. It also demonstrates explicitly how the emergence and stability of center vortices is related to the existence of color screening by gluon fields.

We compare U (1) lattice gauge theory to an effective model of Maxwell and London equations. In the effective model there is only one free parameter, the London penetration depth λ. It turns out that one can get good agreement between both models if one modifies the usual definition of magnetic monopole currents in U (1) lattice gauge theory. This comparison also shows that already at small distances fluctuations of the occuring string are important. Further, we investigate the β-dependence of the penetration depth and determine the suppression of the monopole condensate in flux tubes.

We modify the standard Wilson action of SU (3) lattice gauge theory by adding an extra term which suppresses colour magnetic currents. We present numerical results of simulations at zero and finite temperature and show that colour magnetic currents strongly influence the confining properties of SU (3) lattice gauge theory.

The dually transformed path integral of four-dimensional U (1) lattice gauge theory is used for the calculation of expectation values in the presence of external charges. Applying the dual simulation to flux tubes for charge distances up to around 20 lattice spacings, we find a deviation from the behaviour of a dual type-II superconductor in the London limit at large distances. The roughening of the flux tube agrees with the effective string picture of confinement. Further we show that finite temperature effects are negligible for time extents larger than the charge distance. Finally we analyze the different contributions to the total energy of the electromagnetic field. The parallel component of the magnetic field turns out to have the strongest influence on the deviation from the linear behaviour at small charge distances.

We find, in close analogy to abelian dominance in maximal abelian gauge, the phenomenon of center dominance in maximal center gauge for SU(2) lattice gauge theory. Maximal center gauge is a gauge-fixing condition that preserves a residual Z 2 gauge symmetry; "center projection" is the projection of SU(2) link variables onto Z 2 center elements, and "center dominance" is the fact that the center-projected link elements carry most of the information about the string tension of the full theory. We present numerical evidence that the thin Z 2 vortices of the projected configurations are associated with "thick" Z 2 vortices in the unprojected configurations. The evidence also suggests that the thick Z 2 vortices may play a significant role in the confinement process.

We investigate singly and doubly charged flux tubes in U (1) lattice gauge theory. By simulating the dually transformed path integral we are able to consider large flux tube lengths, low temperatures, and multiply charged systems without loss of numerical precision. We simulate flux tubes between static sources as well as periodically closed flux tubes, calculating flux tube profiles, the total field energy and the free energy. Our main results are that the string tension in both three and four dimensions scales proportionally to the charge -which is in contrast to previous lattice results -and that in four-dimensional U (1) there is an attractive interaction between flux tubes for β approaching the phase transition.

The Dirac operator describing the coupling of continuum quark fields to SU (2) center vortex world-surfaces composed of elementary squares on a hypercubic lattice is constructed. It is used to evaluate the quenched Dirac spectral density in the random vortex world-surface model, which previously has been shown to quantitatively reproduce both the confinement properties and the topological susceptibility of SU (2) Yang-Mills theory. Under certain conditions on the modeling of the vortex gauge field, a behavior of the quenched chiral condensate as a function of temperature is obtained which is consistent with measurements in SU (2) lattice Yang-Mills theory.

We investigate the influence of the granularity of the lattice on the potential between monopoles. Using the flux definition of monopoles we introduce their centers of mass and are able to realize continuous shifts of the monopole positions. We find periodic deviations from the 1/r-behavior of the monopole-antimonopole potential leading to local extrema. We suppose that these meta-stabilities may influence the order of the phase transition in compact QED.

Earlier investigations [Int. J. Mod. Phys. A19, 5017 (2004)] showed local minima in the monopole–antimonopole potential in U(1) gauge theory on the lattice. In this paper we localize monopoles of Monte Carlo configurations. A statistical analysis of localization measurements gives us the probability density which we compare with the potential found in Ref. 1. We find the monopoles mainly located either in the center of three-dimensional cubes or on the interface between two cubes. This agrees with the position of minima and maxima of the monopole–antimonopole potential.

We discuss the derivation of the path integral representation over gauge degrees of freedom for Wilson loops in SU (N ) gauge theory and 4-dimensional Euclidean space-time by using well-known properties of group characters. A discretized form of the path integral is naturally provided by the properties of group characters and does not need any artificial regularization. We show that the path integral over gauge degrees of freedom for Wilson loops derived by Diakonov and Petrov (Phys. Lett. B224 (1989) 131) by using a special regularization is erroneous and predicts zero for the Wilson loop. This property is obtained by direct evaluation of path integrals for Wilson loops defined for pure SU (2) gauge fields and Z(2) center vortices with spatial azimuthal symmetry. Further we show that both derivations given by Diakonov and Petrov for their regularized path integral, if done correctly, predict also zero for Wilson loops. Therefore, the application of their path integral representation of Wilson loops cannot give a new way to check confinement in lattice as has been declared by Diakonov and Petrov (Phys. Lett. B242 (1990) 425). From the path integral representation which we consider we conclude that no new non-Abelian Stokes theorem can exist for Wilson loops except the old-fashioned one derived by means of the path-ordering procedure.

This study introduces a new theoretical framework called the "Theory of Nature," which unifies magnetism, electricity, and light under a single energy form termed "pothu." The theory posits unique properties, such as real-time energy transfer once electricity or light reaches its destination. It addresses fundamental questions about magnetic attraction, repulsion, field line formation, and the instantaneous nature of light and electricity post-transfer. Experimental implications and comparisons with classical physics are discussed, offering a novel perspective on energy interactions. • Why do magnets stick? • Why do magnetic poles repel each other? • Why is the magnetic field stronger in elongated regions? • Why do magnetic fields form lines? • Light takes time to reach its destination, but once it arrives, it operates in real time. The same applies to electricity.

This study introduces a new theoretical framework called the "Theory of Nature," which unifies magnetism, electricity, and light under a single energy form termed "pothu." The theory posits unique properties, such as real-time energy transfer once electricity or light reaches its destination. It addresses fundamental questions about magnetic attraction, repulsion, field line formation, and the instantaneous nature of light and electricity post-transfer. Experimental implications and comparisons with classical physics are discussed, offering a novel perspective on energy interactions. Key Questions • Why do magnets stick? • Why do magnetic poles repel each other? • Why is the magnetic field stronger in elongated regions? • Why do magnetic fields form lines? • Light takes time to reach its destination, but once it arrives, it operates in real time. The same applies to electricity.

Dieses Buch stellt die Weber-De Broglie-Bohm-Theorie (WDBT) vor – eine konsequente Weiterentwicklung etablierter Ansätze, die die Weber-Elektrodynamik (WED) mit der De-Broglie-Bohm-Theorie (DBT) verbindet. Der Kern der WDBT ist radikal einfach: Elektromagnetische Effekte werden nicht durch Felder, sondern durch direkte, geschwindigkeits- und beschleunigungsabhängige Kräfte zwischen Ladungen vermittelt. Kombiniert mit dem nicht-lokalen Quantenpotential der DBT entsteht so ein kohärenter theoretischer Rahmen, der Plasmen, Quantenphänomene und astrophysikalische Prozesse einheitlich erklärt, ohne auf die Ad-hoc-Annahmen klassischer Feldtheorien zurückgreifen zu müssen.

Classifying the phases of gauge theories is hindered by the lack of local order parameters. In particular, the standard Wilson's and 't Hooft's non-local order parameters are known to be insufficient to explain the existence of the plethora of phases that are found in supersymmetric gauge theories. Motivated by these observations, we reanalyze the concept of gauge symmetry breaking using Galois theory. Unlike the ordinary classical notion of unbroken gauge group, the Galois symmetry makes sense in the full quantum theory and must be a phase invariant. The algebraic structure underlying the space of vacua of supersymmetric gauge theories, that we have developed recently, is precisely designed to allow a rigorous mathematical implementation of these ideas.

In this work we investigate q q spectra and wavefunctions of light front transverse lattice Hamiltonians that result from different methods of formulating fermions on the transverse lattice. We adopt the one link approximation for the transverse lattice and Discrete Light Cone Quantization to handle longitudinal dynamics. We perform a detailed study of the continuum limit of DLCQ and associated techniques to manage severe light front infrared divergences. We explore the effects of various parameters of the theory, especially, the strength of the helicity-flip interaction and the link mass on spectra and wavefunctions.

We address the problems of fermions in light front QCD on a transverse lattice. We propose and numerically investigate different approaches of formulating fermions on the light front transverse lattice. In one approach we use forward and backward derivatives. There is no fermion doubling and the helicity flip term proportional to the fermion mass in the full light front QCD becomes an irrelevant term in the free field limit. In the second approach with symmetric derivative (which has been employed previously in the literature), doublers appear and their occurrence is due to the decoupling of even and odd lattice sites. We study their removal from the spectrum in two ways namely, light front staggered formulation and the Wilson fermion formulation. The numerical calculations in free field limit are carried out with both fixed and periodic boundary conditions on the transverse lattice and finite volume effects are studied. We find that an even-odd helicity flip symmetry on the light front transverse lattice is relevant for fermion doubling.

The partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), is expressed as a special instance of the partition function of the 4D Z2 LGT. This unies all classical spin models with apparently very different features in a single complete model. This result is applied to establish a new method to compute the mean-eld theory of Abelian discrete LGTs with d ≥ 4, and to show that computing the partition function of the 4D Z2 LGT is computationally hard (#P hard). The 4D Z2 LGT is also proved to be approximately complete for Abelian continuous models. The proof uses techniques from quantum information.

Let Ω be a m-set, where m > 1, is an integer. The Hamming graph H(n, m), has Ω n as its vertex-set, with two vertices are adjacent if and only if they differ in exactly one coordinate. In this paper, we provide a proof on the automorphism group of the Hamming graph H(n, m), by using elementary facts of group theory and graph theory.

Let Ω be a m-set, where m > 1, is an integer. The Hamming graph H(n, m), has Ω n as its vertex-set, with two vertices are adjacent if and only if they differ in exactly one coordinate. In this paper, we provide a proof on the automorphism group of the Hamming graph H(n, m), by using elementary facts of group theory and graph theory.

We calculate pion mass, pion decay constant, PCAC quark mass and nucleon mass in two flavour lattice QCD with unimproved Wilson fermion and gauge actions. Simulations are performed using DD-HMC algorithm at two lattice spacings and two volumes for several values of the quark mass. The cutoff effects in pion mass and nucleon mass for the explored region of parameter space are found to be negligible. The chiral behaviours of pion mass, pion decay constant and quark condensate are found to be qualitatively consistent with NLO chiral perturbation theory.

We present numerical results for non-compact three-dimensional QED for numbers of flavors N f = 1 and N f = 4. In particular, we address the issue of whether chiral symmetry is spontaneously broken in the continuum limit, and obtain a positive answer for N f = 1, with a dimensionless condensate estimated to be β 2 ψψ ≃ O(10 -3 ), implying that the critical number of flavors N f c > 1. We also compare the N f = 1 and N f = 4 models by analysing the transition from strong to weak coupling behaviour using an equation of state based on a continuous phase transition. While some qualitative differences emerge, it appears difficult to determine whether N f = 4 lies above or below N f c .

We present the most recent results from the FASTSUM collaboration for hadron properties at high temperature. This includes the temperature dependence of the light and charmed meson and baryon spectrum, as well as properties of heavy quarkonia. The results are obtained using anisotropic lattices with a fixed scale approach. We also present the status of our next generation gauge ensembles.

We present the most recent results from the FASTSUM collaboration for hadron properties at high temperature. This includes the temperature dependence of the light and charmed meson and baryon spectrum, as well as properties of heavy quarkonia. The results are obtained using anisotropic lattices with a fixed scale approach. We also present the status of our next generation gauge ensembles.

We study the Thirring model in three spacetime dimensions, by means of Monte Carlo simulation on lattice sizes 8 3 and 12 3 , for numbers of fermion flavors N f = 2, 4, 6. For sufficiently strong interaction strength, we find that spontaneous chiral symmetry breaking occurs for N f = 2, 4, in accordance with the predictions of the Schwinger-Dyson approach. The phase transitions which occur are continuous and with critical scaling behaviour depending on N f . For N f = 6 our results are preliminary, and no firm conclusions about the existence or otherwise of chiral symmetry breaking are possible.

We present results suggesting that magnetic monopoles can account for chiral symmetry breaking in abelian gauge theory. Full U (1) configurations from a lattice simulation are factorized into magnetic monopole and photon contributions. The expectation ψψ is computed using the monopole configurations and compared to results for the full U (1) configurations. It is shown that excellent agreement between the two values of ψψ is obtained if the effect of photons, which "dress" the composite operator ψψ, is included. This can be estimated independently by measurements of the physical fermion mass in the photon background.

We present the first evidence from lattice simulations that the magnetic monopoles in three dimensional compact quantum electrodynamics (cQED 3 ) with N f = 2 and N f = 4 four-component fermion flavors are in a plasma phase. The evidence is based mainly on the divergence of the monopole susceptibility (polarizability) with the lattice size at weak gauge couplings. A weak four-Fermi term added to the cQED 3 action enabled simulations with massless fermions. The exact chiral symmetry of the interaction terms forbids symmetry breaking lattice discretization counter-terms to appear in the theory's effective action. It is also shown that the scenario of a monopole plasma does not depend on the strength of the four-Fermi coupling. Other observables such as the densities of "isolated" dipoles and monopoles and the so-called specific heat show that a crossover from a dense monopole plasma to a dilute monopole gas occurs at strong couplings. The implications of our results on the stability of U(1) spin liquids in two spatial dimensions are also discussed.

We present numerical results for noncompact three-dimensional quantum electrodynamics for numbers of flavors N f = 1 and N f = 4. In particular, we address the issue of whether chiral symmetry is spontaneously broken in the continuum limit, and obtain a positive answer for N f = 1, with a dimensionless condensate estimated to be ␤ 2 ͗ ¯͘ӍO͑10 -3 ͒, implying that the critical number of flavors N fc Ͼ 1. We also compare the N f = 1 and N f = 4 models by analyzing the transition from strong to weak coupling behavior using an equation of state based on a continuous phase transition. While some qualitative differences emerge, it appears difficult to determine whether N f = 4 lies above or below N fc .