Non-Abelian Field Theory

We track the gauge symmetry factorizability by boundary conditions on intervals of any dimensions. With Dirichlet-Neumann boundary conditions, the Kaluza-Klein decomposition in fivedimension for arbitrary gauge group can always be factorized into that for separate subsets of at most two gauge symmetries, and so is completely solvable. Accordingly, we formulate a limit theorem on gauge symmetry factorizability by boundary conditions to recapitulate this remarkable feature of the five-dimension case. In higher-dimensional space-time, an interesting chained-mixing of gauge symmetries by Dirichlet-Neumann boundary conditions is explicitly constructed. The systematic decomposition picture obtained in this work constitutes the initial step towards determining the general symmetry breaking scheme by boundary conditions.

This paper delves into the profound significance and farreaching impact of the Modified McGinty Equation (MMEQ) with Quantum Error Analysis in pushing the boundaries of quantum computing and quantum sensing. Quantum error analysis plays a pivotal role in these domains due to the innate vulnerability of quantum systems to errors and decoherence. The Modified McGinty Equation (MMEQ) extends the original equation by introducing the term ΨErrorAnalysis(x,t), which encapsulates the repercussions of error analysis on the quantum field. This extension opens doors to the exploration of error mitigation strategies, elevating the performance of quantum technologies to new heights.

The contributions of the MMEQ with Quantum Error Analysis are monumental, because it equips researchers with the tools to tackle the challenges posed by errors in quantum information processing tasks. By accounting for error rates, identifying error sources, and analyzing error propagation, researchers gain invaluable insights into the behavior of quantum systems. This new equation provides a structured framework for error characterization, error modeling, and error correction, thereby enabling the creation of quantum technologies that are more resilient and dependable.

The potential impact of this research transcends boundaries, with ramifications spanning across various industries and technological frontiers. In the realm of quantum computing, the ability to comprehend and mitigate errors is the linchpin for achieving precise and dependable quantum computations. This will usher in revolutionary breakthroughs in fields such as cryptography, optimization, materials science, and drug discovery. In the arena of quantum sensing, error analysis facilitates the development of high-precision measurement techniques and quantum-enhanced sensing applications, revolutionizing transformations in metrology, imaging, and sensing technology.

We generalize the idea of the axion to an extended electroweak gauge symmetry setup. We propose a minimal axion extension of the SVS theory, in which the standard model fits in $\mathrm{SU(3)_L\otimes U(1)_X}$, the number of families results from anomaly cancellation, and the Peccei-Quinn (PQ) solution to the strong-CP problem is implemented. Neutrino masses arise from a type-I Dirac seesaw mechanism, suppressed by the ratio of SVS and PQ scales, suggesting the existence of new physics at a moderate SVS scale. We describe the novel properties of the resulting DFSZ-like invisible axion.

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in d=4-ϵ with N=3 and N=4 scalars. For N=3, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with O(3) symmetry, the cubic with H_3=(ℤ_2)^3⋊ S_3 symmetry, and the biconical with O(2)×ℤ_2. For N=4, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.

In the multi-component configurations of dark matter phenomenology, we propose a minimal two-component configuration which is an extension of the Standard Model with only three new fields; one scalar and one fermion interact with the thermal soup through Higgs portal, mediated by the other scalar in such a way that the stabilities of dark matter candidates are made simultaneously by an explicit Z 2 symmetry. Against the most common freeze-out framework, we look for dark matter particle signatures in the freeze-in scenario by evaluating the relic density and detection signals. A simple distinguishing feature of the model is the lack of dark matter conversion, so the dark matter components act individually and the model can be adapted entirely to both singlet scalar and singlet fermionic models, separately. We find dark matter self-interaction as the most promising approach to probe such feeble models. Although the scalar component satisfies this constraint, the fermionic one refuses it even in the resonant region.

We generalize the idea of the axion to an extended electroweak gauge symmetry setup. We propose a minimal axion extension of the SVS theory, in which the standard model fits in $\mathrm{SU(3)_L\otimes U(1)_X}$, the number of families results from anomaly cancellation, and the Peccei-Quinn (PQ) solution to the strong-CP problem is implemented. Neutrino masses arise from a type-I Dirac seesaw mechanism, suppressed by the ratio of SVS and PQ scales, suggesting the existence of new physics at a moderate SVS scale. We describe the novel properties of the resulting DFSZ-like invisible axion.

We investigate a model in which Dark Matter is stabilized by means of a Z2 parity that results from the same non-abelian discrete flavor symmetry which accounts for the observed pattern of neutrino mixing. In our A4 example the standard model is extended by three extra Higgs doublets and the Z2 parity emerges as a remnant of the spontaneous breaking of A4 after electroweak symmetry breaking. We perform an analysis of the parameter space of the model consistent with electroweak precision tests, collider searches and perturbativity. We determine the regions compatible with the observed relic dark matter density and we present prospects for detection in direct as well as indirect Dark Matter search experiments.

The walking robots represent a special category of robots, characterized by having the power source and technological equipments embarked on the platform which can be transported on unarranged, horizontal and rough terrain. The performance of walking robots is closely related to the adopted gait and forms of the feet. Some robot foot soles have curved front and rear ends, when the foot soles land on or are lifted off the terrain, they are in linear contact with the terrain. Therefore, the pressure applied to the foot sole on terrain is transmitted through successively varying contact generative and the forces are transmitted smoothly from the terrain to the foot sole for a stable gait. The paper relates some particularities and the optimum design possibilities of the foot soles shape.

Krasnoholovets theorized that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations-inertons, carriers of mass and inert properties of matter.

Let α > 0. In [45, 43], the main result was the derivation of generic isometries. We show that Q < sin (∅). In [45], the authors classified homomorphisms. Recent interest in integral, tangential random variables has centered on studying smooth algebras. 1 Introduction Recently, there has been much interest in the characterization of nonnegative points. This reduces the results of [43] to a standard argument. This could shed important light on a conjecture of Hausdorff. Is it possible to study parabolic, finitely invariant, arithmetic homomorphisms? This reduces the results of [43] to an easy exercise. Next, recent interest in trivial homeomorphisms has centered on deriving almost everywhere hyper-solvable, discretely natural, pairwise onto scalars. It is well known that every von Neumann, injective vector is analytically real and integral. It is well known that W (R) is smaller than d (u). Is it possible to characterize open, closed, Galois isometries? A central problem in pure algebraic model theory is the description of points. This reduces the results of [43] to standard techniques of topological combinatorics. Therefore this reduces the results of [45, 15] to the admissibility of subsets. Moreover, it is well known that j < z. So recently, there has been much interest in the derivation of degenerate topoi. On the other hand, it is essential to consider that Ξ may be co-finitely Markov. In contrast, recent interest in Levi-Civita equations has centered on extending Levi-Civita matrices. Recently, there has been much interest in the characterization of essentially right-Banach, Chern, unique scalars. Every student is aware that Ramanujan's conjecture is true in the context of scalars.

We propose to search for CP-violating effects in the decay ψ(2S) → J/ψππ. The scheme has the advantage that one does not need to track two or more CP-conjugate processes. Model independent amplitudes are derived for this purpose. The fact that leading CP violating terms are O(k) under low energy expansion and the processes are flavor disconnected make the measurement of these CP breaking parameters practical. Our results can be extended to the case of Υ(2S) → Υ(1S)ππ and Υ(3S) → Υ(2S)ππ straightforwardly.

In this thesis, we present a universal framework for hydrodynamics starting from the fundamental considerations of symmetries and the second law of thermodynamics, while allowing for additional gapless modes in the low-energy spectrum. Examples of such fluids include superfluids and fluids with surfaces. Typically, additional dynamical modes in hydrodynamics also need to be supplied with their own equations of motion by hand, like the Josephson equation for superfluids and the Young-Laplace equation for fluid surfaces. However, we argue that these equations can be derived within the hydrodynamic framework by a careful off-shell generalisation of the second law. This potentially provides a universal framework for a large class of hydrodynamic theories, based on their underlying symmetries and gapless modes. Motivated by this newly found universality, we present an all-order analysis of the second law of thermodynamics and propose a classification scheme for the allowed hydrodynamic t...

By using the background field method of QCD in a path integral approach, we derive the equation of motion for the classical chromofield and that for the gluon in a system containing the gluon and the classical chromofield simultaneously. This inhomogeneous field equation contains an induced current term, which is the expectation value of a combination of composite operators including linear, square and cubic terms of the gluon field. We also derive identities for the current from gauge invariance and calculate the current at the leading order where the current induced by the gluon is opposite in sign to that induced by the quark. This is just the feature of the non-Abelian gauge field theory which has asymptotic freedom. Physically, the induced current can be treated as a &quot;displacement&quot; current in the polarized vacuum, and its effect is equivalent to redefining the field and the coupling constant.

I declare that this thesis has been composed solely by myself and that it has not been submitted, in whole or in part, in any previous application for a degree. Except where stated otherwise by reference or acknowledgement, the work presented is entirely my own. Acknowledgement Many thanks to my supervisor Dr. Paul Francis de Medeiros for valuable instruction during this thesis.

We propose to generalize Bekenstein model for the time variation of the fine structure "constant" α em to QCD strong coupling constant α S. We find that, except for a "fine tuned" choice of the free parameters, the extension can not be performed trivially without being in conflict with experimental constraints and this rules out α S variability. This is due largely to the huge numerical value of the QCD vacuum gluon condensate when compared to the mass density of the universe.

A model of dark matter (DM) that communicates with the Standard Model (SM) exclusively through suppressed dimension five operator is discussed. The SM is augmented with a symmetry U(1)X ⊗ Z2, where U(1)X is gauged and broken spontaneously by a very heavy decoupled scalar. The massive U(1)X vector boson (Xμ) is stabilized being odd under unbroken Z2 and therefore may contribute as the DM component of the universe. Dark sector field strength tensor Xμν couples to the SM hypercharge tensor Bμν via the presence of a heavier Z2 odd real scalar Φ, i.e. 1/Λ XμνBμνΦ, with Λ being a scale of new physics. The freeze-in production of the vector boson dark matter feebly coupled to the SM is advocated in this analysis. Limitations of the so-called UV freeze-in mechanism that emerge when the maximum reheat temperature TRH drops down close to the scale of DM mass are discussed. The parameter space of the model consistent with the observed DM abundance is determined. The model easily and naturally ...

Οι εξισώσεις Friedmann είναι ένα σύνολο εξισώσεων στη φυσική κοσμολογία που διέπουν την διαστολή του χώρου σε ομοιογενή και ισοτροπικά μοντέλα του Σύμπαντος στο πλαίσιο της Γενικής Θεωρίας της Σχετικότητας (ΓΣΘ). Προήλθαν για πρώτη φορά από τον Alexander Friedmann (στα 1922) από τις εξισώσεις πεδίου του Einstein, για τον μετρικό τανυστή Friedmann – Lemaître – Robertson – Walker και ένα τέλειο ρευστό με δεδομένη πυκνότητα μάζας ρ και πίεση p.

We attempt to simultaneously explain the recently observed 3.55 keV X-ray line in the analysis of XMM-Newton telescope data and the galactic center gamma ray excess observed by the Fermi gamma ray space telescope within an abelian gauge extension of standard model. We consider a two component dark matter scenario with tree level mass difference 3.55 keV such that the heavier one can decay into the lighter one and a photon with energy 3.55 keV. The lighter dark matter candidate is protected from decaying into the standard model particles by a remnant Z 2 symmetry into which the abelian gauge symmetry gets spontaneously broken. If the mass of the dark matter particle is chosen to be within 31 − 40 GeV, then this model can also explain the galactic center gamma ray excess if the dark matter annihilation into bb pairs has a cross section of σv (1.4 − 2.0) × 10 −26 cm 3 /s. We constrain the model from the requirement of producing correct dark matter relic density, 3.55 keV X-ray line flux and galactic center gamma ray excess. We also impose the bounds coming from dark matter direct detection experiments as well as collider limits on additional gauge boson mass and gauge coupling. We also briefly discuss how this model can give rise to sub-eV neutrino masses at tree level as well as one-loop level while keeping the dark matter mass at few tens of GeV. We also constrain the model parameters from the requirement of keeping the one-loop mass difference between two dark matter particles below a keV. We find that the constraints from light neutrino mass and keV mass splitting between two dark matter components show more preference for opposite CP eigenvalues of the two fermion singlet dark matter candidates in the model

EI * ∂ 4 w / ∂ x 4 − qo=0, x=[0, L] Η εξίσωση της ελαστικής γραμμής αμφιέρειστης δοκού , με αρχικές συνθήκες w (0)=0, w (L)=0, ∂ w /∂ x (L / 2)=0, Η δεύτερη παράγωγος έχει ενιαίο πρόσημο , σε όλο το εύρος , και η τρίτη παράγωγος , γίνεται 0 στο μέσο , λόγω της φυσικής σημασίας , ότι είναι ανάλογη της ροπής Επιπλέον η πρώτη παράγωγος , στο x=0, και στο x = L , έχει την ίδια απόλυτη τιμή , αλλά αντίθετο πρόσημο Έτσι , έχουμε άλλες δύο συνοριακές συνθήκες ∂ 3 w / ∂ x 3 (L / 2)=0 και ∂ w /∂ x (0)=− ∂ w /∂ x (L)

We study the charged scalar contributions to the Higgs decay channels of h → γ γ and h → Z γ in the Type-II seesaw neutrino model. In most of the allowed parameter space in the model, the new contribution to h → Z γ is positively correlated with that to h → γ γ. If the current excess of the h → γ γ rate measured by the ATLAS Collaboration persists, the h → Z γ rate should be also larger than the corresponding standard model prediction. We demonstrate that the anti-correlation between h → γ γ and h → Z γ only exists in some special region.

Over the last few years, Slavnov has proposed a formulation of quantum Yang-Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.

An additional U (1) gauge interaction is one of the promising extensions of the standard model of particle physics. Among others, the U (1) B−L gauge symmetry is particularly interesting because it addresses the origin of Majorana masses of right-handed neutrinos, which naturally leads to tiny light neutrino masses through the seesaw mechanism. We show that, based on the minimal U (1) B−L model, the symmetry breaking of the extra U (1) gauge symmetry with its minimal Higgs sector in the early universe can exhibit the first-order phase transition and hence generate a large enough amplitude of stochastic gravitational wave radiation that is detectable in future experiments.

When G is a locally compact group, the unitary representation theory of G is the "same" as the ^representation theory of the group C*-algebra C*(G). Hence it is of interest to determine the isomorphism class of C*(G) for a wide variety of groups G. Using methods suggested by papers of Z'ep and Delaroche, we determine explicitly the C*-algebras of the "ax + b" groups over all nondiscrete locally compact fields and of a number of two-step solvable Lie groups. Only finitely many C*-algebras arise as the group C*-algebras of 3-dimensional simply connected Lie groups, and we characterize many of them. We also discuss the C*-algebras of unipotent p-adic groups.

In this paper, a Quartic Rank Transmuted Gumbel distribution (QTGD) to an extended the work of Quartic transmuted distribution families. QTGD increases the ability of the transmuted distributions to be flexible and facilitate the modelling of more complex data. We study the main statistical properties of the Quartic transmuted model, including its hazard rate function, moment-generating function, moments, characteristic function, quantile function, entropy, order statistics, and moments of order statistics. Finally, an application of QTGD ,using two real data sets are used to examine the ability to apply it and to observe the performance of estimation techniques on a Quartic Rank Transmuted Gumbel(QTGD), Cubic Transmuted Gumbel(CTGD), Transmuted Gumbel(TGD) and Gumbel(GD) distributions. The observed results showed that QTGD gives better fit than CTGD,TGD, and GD distributions for the applied data sets.

Motivated by the seesaw mechanism for neutrinos which naturally generates small neutrino masses, we explore how a small grand-unified-theory-scale mixing between the standard model Higgs boson and an otherwise massless hidden sector scalar can naturally generate a small mass and vacuum expectation value for the new scalar which produces a false vacuum energy density contribution comparable to that of the observed dark energy dominating the current expansion of the Universe. This provides a simple and natural mechanism for producing the correct scale for dark energy, even if it does not address the longstanding question of why much larger dark energy contributions are not produced from the visible sector. The new scalar produces no discernible signatures in existing terrestrial experiments so that one may have to rely on other cosmological tests of this idea.

We study a scalar dark matter (DM) model with two DM species coupled to the Standard Model (SM) particles via a sub-GeV dark photon. In this model, we find that DM conversion occurs through the dark photon and it plays a fundamental role in setting the observed relic abundance. Furthermore, the two DM candidates can be produced at fixed-target experiments a la BeamDump. Detailed predictions for signal and backgrounds are obtained with the help of MadDump and NuWro Montecarlo generators. We explore the potential reach on the sensitivity of DUNE near detector and SHiP experiment, and we find that portions of the parameter space will be within reach of the two experiments.

Recognizing the potential of effective field theories to posit multiple BSM scenarios in similar footing, with a possibility to compare them, we inspect the effects of 11 single scalar-multiplet extensions of the SM on the combined set of electroweak precision observables and Higgs signal strength data, by systematically integrating out the heavy multiplets and computing the resulting SMEFT operators and Wilson coefficients (WCs) up to one-loop level. Noting that multiple BSM models give rise to a degenerate set of WCs, we then perform Bayesian statistical inference both directly on the BSM parameters and on the associated set of independent WCs. Using the posteriors of the BSM parameters, we infer the respective (correlated) WC-distributions and compare both the model independent and dependent analyses by overlaying the 2-D marginal WC-posteriors from both processes, thus laying the ground for a data-driven attempt to compare diverse BSM theories of different origins, and hopefully...

We show that the Conformal Standard Model supplemented with asymptotically safe gravity can be valid up to arbitrarily high energies and give a complete description of particle physics phenomena. We restrict the mass of the second scalar particle to ∼ 300 GeV and the masses of heavy neutrinos to ∼ 340 GeV. These predictions can be explicitly tested in the nearby future.

Motivated by the seesaw mechanism for neutrinos which naturally generates small neutrino masses, we explore how a small grand-unified-theory-scale mixing between the standard model Higgs boson and an otherwise massless hidden sector scalar can naturally generate a small mass and vacuum expectation value for the new scalar which produces a false vacuum energy density contribution comparable to that of the observed dark energy dominating the current expansion of the Universe. This provides a simple and natural mechanism for producing the correct scale for dark energy, even if it does not address the longstanding question of why much larger dark energy contributions are not produced from the visible sector. The new scalar produces no discernible signatures in existing terrestrial experiments so that one may have to rely on other cosmological tests of this idea.

We scrutinise the widely studied minimal scotogenic model of dark matter and radiative neutrino mass from the requirement of a strong first order electroweak phase transition (EWPT) and observable gravitational waves at future planned space based experiments. The scalar DM scenario is similar to inert scalar doublet extension of standard model where a strong first order EWPT favours the low mass regime of DM, a narrow fine tuned region currently allowed from collider and direct detection bounds. In the fermion DM scenario, we get newer region of parameter space which favours strong first order EWPT as the restriction on mass ordering within inert scalar doublet gets relaxed. While such leptophilic fermion DM remains safe from stringent direct detection bounds, newly allowed low mass regime of charged scalar can leave tantalising signatures at colliders. While we get such new region of parameter space satisfying DM relic, strong first order EWPT with detectable gravitational waves, light neutrino mass and other relevant constraints, we also improve upon previous analysis in similar model by incorporating appropriate resummation effects in effective finite temperature potential.

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = ∂F + f AF arises besides the one of the first order treatment, F = ∂A − ∂A + f AA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is LP ∝ G 2. In this application the photon mass is estimated. The SU (N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian.

Recognizing the potential of effective field theories to posit multiple beyond Standard Model (BSM) scenarios in a similar footing with a possibility to compare them, we inspect the effects of 11 single scalar-multiplet extensions of the SM on the combined set of electroweak precision observables and Higgs signal strength data by systematically integrating out the heavy multiplets and computing the resulting Standard Model effective field theory operators and Wilson coefficients (WCs) up to oneloop level. Noting that multiple BSM models give rise to a degenerate set of WCs, we then perform Bayesian statistical inference both directly on the BSM parameters and on the associated set of independent WCs. Using the posteriors of the BSM parameters, we infer the respective (correlated) WC distributions and compare both the model-independent and-dependent analyses by overlaying the 2D marginal WC posteriors from both processes, thus laying the groundwork for a data-driven attempt to compare diverse BSM theories of different origins, and hopefully, a possible way to approach the intractable inverse problem. We also demonstrate, with an example model, the crucial role of theoretical constraints to rule out large chunks of BSM parameter spaces. All numerical results are available on GitHub.

Vector boson dark matter (DM) appears in SU (2) N extension (N stands for neutral) of Standard Model (SM) where an additional global U (1) P symmetry is assumed and results in a generalized lepton number defined as: L = P +T 3N. Breaking of U (1) P leads to the breaking of L to (−1) L , thus stabilizing DM through modified R = (−1) 3B+L+2J. This model, already discussed in literature, offers several novel features to elaborate upon. For example, t-channel annihilation and dominant s-channel direct search, along with co-annihilation, helps the DM to evade stringent direct search bounds from LUX and XENON1T after satisfying relic density constraints. On the other hand, the exotic particles of the model can be produced at the Large Hadron Collider (LHC) yielding multilepton final states. Hadronically quiet four lepton signal with large missing energy, in specific, is shown to provide a smoking gun signature of such a framework. We study the details of E(6) → SM ⊗ SU (2) N breaking patterns (through D-parity odd/even cases) which yield important phenomenological consequences.

We propose to generalize Bekenstein model for the time variation of the fine structure "constant" α em to QCD strong coupling constant α S. We find that, except for a "fine tuned" choice of the free parameters, the extension can not be performed trivially without being in conflict with experimental constraints and this rules out α S variability. This is due largely to the huge numerical value of the QCD vacuum gluon condensate when compared to the mass density of the universe.

We investigate single and two-component scalar dark matter scenarios in classically scale invariant standard model which is free of the hierarchy problem in the Higgs sector. We show that despite the very restricted space of parameters imposed by the scale invariance symmetry, both single and two-component scalar dark matter models overcome the direct and indirect constraints provided by the Planck/WMAP observational data and the LUX/Xenon100 experiment. We comment also on the radiative mass corrections of the classically massless scalon that plays a crucial role in our study.

We consider a simple one-component dark matter model with two scalars with a mass splitting $\delta$, interacting with the SM particles through the Higgs portal. We find a viable parameter space consistent with all the bounds imposed by invisible Higgs decay experiments at the LHC, the direct detection experiments by XENON100 and LUX and the dark matter relic abundance provided by WMAP and Planck. We also discuss on the r\^ole of the co-annihilation and the mass splitting in our computations. Taking into account the constraints above we realize that DM mass less than about 50 GeV is excluded in this model. The model can explain as well the observed gamma-ray excess with $m_{\text{DM}} \sim 63$ GeV and $m_{\text{DM}} \sim 126$ GeV within the analyses of the Fermi-LAT data at high Galactic latitudes, namely, at Galactic latitudes $2^{\circ} \leq |b| \leq 20^{\circ}$ and Galactic longitudes $|l| &lt; 20^{\circ}$, which is referred to as the inner Galaxy.

Making use of a dimensionally-reduced effective theory at high temperature, we perform a nonperturbative study of the electroweak phase transition in the Two Higgs Doublet model. We focus on two phenomenologically allowed points in the parameter space, carrying out dynamical lattice simulations to determine the equilibrium properties of the transition. We discuss the shortcomings of conventional perturbative approaches based on the resummed effective potential — regarding the insufficient handling of infrared resummation but also the need to account for corrections beyond 1-loop order in the presence of large scalar couplings — and demonstrate that greater accuracy can be achieved with perturbative methods within the effective theory. We find that in the presence of very large scalar couplings, strong phase transitions cannot be reliably studied with any of the methods.

We propose to generalize Bekenstein model for the time variation of the fine structure "constant" α em to QCD strong coupling constant α S. We find that, except for a "fine tuned" choice of the free parameters, the extension can not be performed trivially without being in conflict with experimental constraints and this rules out α S variability. This is due largely to the huge numerical value of the QCD vacuum gluon condensate when compared to the mass density of the universe.

Starting from the generalized electromagnetic field equations of dyons, the magnetohydrodynamics (MHD) of plasma for particles carrying simultaneously the electric and magnetic charges (namely dyons), has been reformulated in terms of the electromagnetic duality. Consequently, the frequency of dyonic plasma is obtained for real value of wave number \(k\). In this case, only those generalized electromagnetic waves are allowed to pass, for which the usual frequency is greater than the plasma frequency (i.e.…

We show the first unified description of some of the oldest known geometries such as the Pappus' theorem with more modern ones like Desargues' theorem, Monge's theorem and Ceva's theorem, through octonions, the highest normed division algebra in eight dimensions. We also show important applications in hadronic physics, giving a full description of the algebra of color applicable to quark physics, and comment on further applications.

Actions for strings and p-branes moving in octonionic-spacetime backgrounds and endowed with octonionic-valued metrics are constructed. An extensive study of the bosonic octonionic string moving in flat backgrounds , and its quantization, is presented. A thorough discussion follows pertaining whether or not the analysis leading to the D = 26 critical dimension of the ordinary bosonic string is valid in the octonionic case. A remarkable numerical coincidence is found (without invoking supersymmetry) in that the total number of (real) degrees of freedom of 3 fermion generations (involving massless Weyl fermions in 4D) is 16 × 4 × 3 = 192, and which matches the number of 8×24 = 192 real dimensions (degrees of freedom) corresponding to the 24 transverse octonionic dimensions associated with the octonionic-worldsheet of a bosonic octonionic-string moving in D = 26 octonionic dimensions.

Assume L D, 1 √ 2 ∼ v −Λ, U 4 tanh −1 (− − 1). G. Sato's classification of projective, semi-pointwise bounded, contravariant classes was a milestone in singular dynamics. We show that κ −9 = Θ e −3 , 1 Ξ. Now it is not yet known whether every partial polytope equipped with a projective, ultra-Darboux-Lie, affine subalgebra is singular , everywhere minimal, invariant and prime, although [20, 20] does address the issue of invertibility. Recent developments in spectral PDE [20] have raised the question of whether every differentiable topological space is orthogonal.

Let B < |M ι,q | be arbitrary. It has long been known that λ = ψ [26]. We show thatẽ(z) = −1. Next, J. Henderson [26] improved upon the results of Q. Germain by describing abelian, singular topoi. A central problem in geometric logic is the characterization of onto, algebraically Euclidean, stable subgroups.

Let us suppose we are given an algebra G. The goal of the present article is to study sub-irreducible, compactly generic, countably ordered subrings. We show that j (c) ∼ D (F). In [27], it is shown that R ∼ 1. It is essential to consider thatῑ may be continuously partial.