Quark confinement

The range of Dr. Subrahmanyan Chandrasekhar's contributions to astrophysics, fluid dynamics, radiation, general relativity, and quantum theory became so extensive that it would require an entire chapter merely to enumerate them. Numerous concepts, institutions, and inventions, including the Chandrasekhar Limit and the Chandra X-Ray

A potential model for mesons is presented, which combines quark confinement and strong decay in a realistic approach. The multichannel Schrodinger formalism is employed to describe a system of one or more permanently closed quark-antiquark channels in interac- tion with several two-meson channels. For the potential in the qq channels a harmonic os- cillator with constant frequency is taken. As for the meson channels only Okubo-Zweig- Iizuka-rule-allowed decays into two mesons of the pseudoscalar or vector type are con- sidered. Final-state interactions between these mesons are not yet taken into account. The communication between confined and free channels is supposed to take place via the 'I'0 mechanism, for which a locally approximated transition potential is derived. In order to ob- tain an analytic solution for the S matrix, the transition potential is treated by using a multi-5-shell method. Kinematically relativistic corrections and color splitting allow a fair- ly successful treatment of pseudoscalar as well as vector mesons for all quark flavors. The results are confronted with the data and discussed.

Baryon resonance form factors can provide valuable information about the QCD structure of nucleons, especially when combined with information from other exclusive reactions such as high momentum transfer elastic scattering, real and virtual Compton scattering and meson electroproduction. Recently, several experiments at Jefferson Lab have measured form factors for the delta(1232) and S11(1535) resonances for maximum Q^2 of greater than 7 GeV^2/c^2. The latest results of these experiments will be presented and the connections with other exclusive reactions such as elastic scattering form factors in terms of common nucleon structure within the framework of generalized parton distributions will be shown.

This paper presents a comprehensive exploration of the Information-Cognitive Compression Field (ICCF) framework, providing a unified theory that connects particle physics, quantum mechanics, general relativity, and cosmology. Through a detailed mathematical formulation, the ICCF theory reveals the geometric origin of the strong interactions, deriving the SU(3) symmetry as a consequence of causal compression dynamics. We further introduce a novel description of quark confinement and hadron mass calculation, based on first principles, and predict new exotic particles such as the 41.2 GeV particle and causally folded state hadrons. The theory also provides insight into the dynamics of quantum measurement, proposing a non-linear recursive collapse mechanism. With experimental predictions that can be tested through high-energy physics and cosmological observations, the ICCF framework presents a groundbreaking approach to fundamental physics, offering potential solutions to longstanding questions about dark matter, dark energy, and quantum gravity.

The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. Light-front holography is a remarkable feature of AdS/CFT: it allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates and the behavior of the QCD coupling in the infrared. We suggest that the spatial support of QCD condensates is restricted to the interior of hadrons, since they arise due to the interactions of confined quarks and gluons. Chiral symmetry is thus broken in a limited domain of size 1/m π , in analogy to the limited physical extent of superconductor phases. A new method for computing the hadronization of quark and gluon jets at the amplitude level, an event amplitude generator, is outlined.

This paper investigates fractional harmonic numbers n i , which determine fractional harmonic in the ∇U model, where m i = n i hF 0 , with a fundamental energy hF 0 ≈ 8.62 MeV. We analyze potential causes of the fractional nature of n i , including topological charges, dynamical effects, quantum numbers, and geometric factors such as fractality and holonomy. Additionally, we explore connections with the *Granda Constant* (F 0 ≈ 1.31 × 10 19 Hz), proposed as the stability threshold for physical forms. Using reverse harmonic decomposition, we test hypotheses about the nature of n i with data from mesons, baryons, resonances, tetraquarks, and pentaquarks. Results highlight the role of topological nodes and spin anharmonicity, while an ontological interpretation within Meta-Monism links fractional n i to the incompleteness of distinction retention. We propose experimental tests and visualizations for further investigation.

The ∇U model, rooted in metamonist ontology, unifies the strong interaction, quantum gravity, and dark energy via topological knots, eliminating gluons. Quark complexes are phase knots, explaining confinement, lifetimes (neutron ∼ 880 s, π ± ∼ 2.6 × 10-8 s, π 0 ∼ 8.48 × 10-17 s, Σ 0 ∼ 7.4 × 10-20 s, Σ + ∼ 8.02 × 10-11 s, Λ ∼ 2.628 × 10-10 s, Ξ 0 ∼ 2.895 × 10-10 s), masses (including Ω-, Λ c , Ξ c , Ω c , D * s with δ s ≈ 0.934, δ c ≈ 0.92), and azimuthal anisotropies (v 2 ≈ 0.06-0.07). The Granda Constant (F 0 ≈ 1.31 × 10 19 Hz) links the QCD mass gap to cosmology. An SU(3)-invariant Lagrangian with CP violation (θ CP ≈ 7.05 × 10-11) and chiral symmetry is constrained by EDM and decays (K 0 → ππ, B → Kπ, D → Kπ, t → W b, D s → ϕπ, B s → J/ψϕ, B c → J/ψπ, D 0 → K-π + , Λ b → ΛJ/ψ, Λ c → pK-π + , Υ(4S) → B 0 B0). The Chaos-Polytope X k,n links θ CP to facet structures, with suppression factors κ ss ≈ 6.14 × 10-8 , κ bs ≈ 5.83 × 10-10 , κ cs ≈ 10-9 , κ ts ≈ 1.2 × 10 6 • exp(-S inst). Verification shows 0.01-2.6% agreement, with Ω-, Λ c , Ξ c , Ω c , D * s improved to ∼ 0.5% via topological data analysis (TDA). New tests include A CP (Λ c) ≈ 3.2 × 10-5 , A CP (Υ(4S)) ≈ 10-4 , quantum tomography, gravitational polarization (P g (Ω-) ≈ 10-15), gravitational decay modulation, and K 0-K0 oscillations (∆m K ≈ 10-18 eV). The model extends to quantum gravity, supersymmetry, and biology (DNA as ∇U knots).

The solitons and kinks of the generalized sl(3,C) sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the tau functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the sl(3,C) affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized sl(3,C) sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U (1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for "quark" confinement.

The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N = 1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.

This paper presents a conceptual analysis of virtual W boson interactions with nearby particles during beta decay. Grounded in quantum field theory, it explores how the transient presence of virtual W bosons influences decay dynamics and local quantum field behavior. Rather than engaging in formal derivations, the study focuses on the qualitative role of energy and momentum exchange mediated by virtual bosons. By connecting theoretical insights to known experimental phenomena, this analysis aims to deepen the understanding of weak interaction mechanisms and their broader significance in particle physics.

The Kaundinya Unified Theory of Everything (KUTE) provides a framework for unifying cosmology, quantum mechanics, and gravity through three foundational axioms. Axiom 1 describes nested radical dynamics driven by local CP violations, governing cosmological phase transitions. Axiom 2 introduces quantum mediators, including Majorana spinors, Higgs and axion fields, loops, and modular forms, facilitating dimensional reduction. Axiom 3 quantizes spacetime into tensor networks at critical density thresholds. A master equation synthesizes these axioms, resolving singularities, the hierarchy problem, and the emergence of quantum gravity while predicting observable phenomena such as axion masses, gravitational wave signatures, and neutrino mass hierarchies.

This paper presents in a concise way the mathematical models and calculation results of states of matter dynamics (gasses, fluids, solids) and phase transitions from thermodynamical viewpoint. In Part A we present the state-of-the-art phase transition thermodynamics and Landau theory. Chap. 1-3 describe the basics of statistics, of phase transitions, and partition function. Chap. 4 describes the generalized Landau theory of phase transitions. Chap. 5-9 present different models and their phase transitions: the magnetic Ising model, the vdWaals fluid-gas, the Lennard-Jones substance, the dipole substance, and the ionic substance. Chap. 11 deals with molecular and continnum fluid-gas dynamics: Boltzmann equation, Navier-Stokes and Euler equations. In Part B we introduce a new ansatz for the partition function, based on the generalized Landau theory, and apply it to two intermolecular potentials : Lennard-Jones and dipole-dipole. For these two potentials, we derive the basic thermodynamical variables: partition function, free energy, pressure, then equation-of-state, saturation curve, characteristic points, and compare the results with experimental data.

In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed.

We derive a gauge-invariant low-energy effective model of the SU(2) Yang-Mills theory. We find that the effective gluon propagator belongs to the Gribov-Stingl type, irrespective of the gauge choice. In the maximally Abelian gauge, especially, we demonstrate that the model exhibits both quark confinement and gluon confinement: the Wilson loop average has area law and the Schwinger function violates reflection positivity. Moreover, we give a formula for the string tension calculable from the gluon propagator of the gauge-invariant field strength and gives a good estimate for the string tension. We discuss if quark confinement and gluon confinement are of the same origin attributed to the gluon propagator in the deep infrared momentum region.

We propose a new reformulation of Yang-Mills theory in which three-and four-gluon self-interactions are eliminated at the price of introducing a sufficient number of auxiliary fields. We discuss the validity of this reformulation in the possible applications such as dynamical gluon mass generation, color confinement and glueball mass calculation. Moreover, we set up a new 1/N c color expansion in the SU (N c ) Yang-Mills theory based on this reformulation. In fact, we give the Feynman rules of the 1/N c expansion in the manifestly Lorentz covariant gauge. The Yang-Mills theory is defined on a non-trivial vacuum where color-singlet transverse gluon pair condensations take place by the attractive gluonic self-interactions. This vacuum condensation provides a common non-vanishing mass for all the gluons with color symmetry being preserved. It is shown that the auxiliary fields become dynamical by acquiring the kinetic term due to quantum corrections. Then the static potential between a pair of color charges is derived as a combination of the Yukawa-type potential and the linear potential with non-vanishing string tension. The mass of the lightest scalar glueball is calculated as the ratio to the gluon mass. The explicit calculations are performed as a partial resummation of the leading order diagrams for the small 't Hooft coupling.

We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU(2) Yang-Mills theory under the Cho-Faddeev-Niemi decomposition. We point out that the generated gluon mass can cure the instability of the Savvidy vacuum. In fact, such a novel type of magnetic condensation is shown to occur by calculating the effective potential. This enables us to explain the infrared Abelian dominance and monopole dominance by way of a non-Abelian Stokes theorem, which suggests the dual superconductivity picture of quark confinement. Finally, we discuss the implication to the Faddeev-Skyrme model with knot soliton as a low-energy effective theory of Yang-Mills theory.

I clarify and or correct certain sentences and expressions in the 2nd Edition released in April 2022. Compared to the 1st Edition (2012), the 2022 release is revised to include topics developed in the last decade. Part III containing problems with solutions is also added.

The positive-plaquette Manton action at weak coupling is a reasonable action for short-distance phenomena. We propose an iterative scheme for evolving this action into an effective action for longer distance scales. We report on the first step of this scheme in which we have measured "blocked" Creutz ratios with lattice spacing 2a at β = 16 on a 32 4 lattice and have searched for an effective action that yields the same ratios on a 16 4 lattice. We also suggest a mechanism for quark confinement that relies upon the lightness of the u and d quarks and formulate a way of testing it in lattice simulations of QCD.

Understanding the spectrum of resonances is directly related to fundamental features of the QCD like the confinement • Photoproduced meson systems are more likely (than eg. pionproduced) to carry exotic quantum numbers Reliable models are badly needed to describe the wealth of the resonance photoproduction data to be expected in near future from JLab (CLAS12 and GlueX), ELSA, MAMI, and SPring-8 experiments

Despite these difficulties, Yukawa's ~ilocal field theory had the attention of several authors who extended the idea and amended its difficulties. Rayski suggested th~ idea of space-time quantization (6). ~larkov introduced "dynamically deformable form factors" to avoid the ' I .

This paper presents a theoretical framework that redefines the process of observation as an active,
non-neutral transaction that leads to structural collapse through the accumulation of informational
tension. Based on the Information Energy Phase Transition Theory (IEPT), and its extension via
the Collapsing Causality through Structural Tension (CCST) model, we introduce a dual-tensor
formulation in which the predictive structure (ΛF ) and the observational structure (ΛC) interact
via accumulated tension density (ρT ). Structural collapse is shown to occur when the integrated
tension
R
ρT (s)ds surpasses a critical threshold, leading to the generation of topological singularities
(Φ1–Φ3) that manifest as energetic gradients, asymmetric rotations, and torsion.
We further derive an observational energy conservation law:
ΔEobs = Ecollapse − Ebeam =
Z
ρT (s) ds
and demonstrate that excluding the contribution of observation energy (Ebeam) results in the reversal
of causality. Through analysis of lattice QCD data (Phys. Rev. Lett. 134, 071901), we
extract topological response values and show that u-quarks exhibit a total accumulated tension
ΔΦtotal ≈ 0.56, aligning with the collapse energy Ecollapse ≈ 0.5–0.6 GeV. These findings validate
the hypothesis that observation-induced torsion is the driver of structural phase transitions.
The proposed framework integrates and extends existing quantum measurement theories—such as
decoherence, POVM, and quantum jumps—by geometrizing observation as a physically meaningful
transformation in tensor space. IEPT thus offers a unified, topological interpretation of collapse
phenomena and challenges the long-held assumption of observational neutrality. Observation, in
this model, is not passive but generates irreversible structure through energetic and informational
flow.

We make the case that the Coulomb-plus linear quark confinement potential predicted by lattice QCD is an approximation to the exactly solvable trigonometric Rosen-Morse potential that has the property to interpolate between the Coulomb-and the infinite wells. We test the predictive power of this potential in the description of the nucleon (considered as a quark-diquark system) and provide analytic expressions for its mass spectrum and the proton electric form factor. We compare the results obtained in this fashion to data and find quite good agreement. We obtain an effective gluon propagator in closed form as the Fourier transform of the potential under investigation.

The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N = 1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.

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The quark matter equation of state (EOS) derived from the standard Nambu -Jona-Lasinio (NJL) model is soft enough to render neutron stars (NS) unstable at the onset of the deconfined phase, and no pure quark matter can be actually present in its interior. Since this is a peculiarity of the NJL model, we have studied a modified NJL model with a momentum cut-off which depends on the density. This procedure, which improves the agreement between QCD and NJL model at large density, modifies the standard NJL equation of state, and then it is potentially relevant for the stability analysis of neutron stars. We show that also within this approach, the NS instability still persists, and that the vacuum pressure, as a signal of quark confinement, has a fundamental role for the NS stability. In this respect, our conclusions point to a relationship between confinement and NS stability.

In this Letter-of-Intent we propose to measure the magnetic form factor of the neutron using the 11 GeV electron beam in the upgraded CEBAF and CLAS12 detector. The measurement will cover the range Q2 = 2 − 14 GeV2. The neutron’s magnetic form factor is one of the fundamental quantities of nuclear physics and its value is an important constraint for the newly-developed generalized parton distributions that hold the promise of dramatically expanding our understanding of the nucleon. The form factors are also important challenges for lattice QCD to meet. This measurement is part of a broad assault on the four elastic nucleon form factors at Jefferson Lab. We will use the ratio of elastic e − n to elastic e − p scattering on deuterium. The ratio method is less vulnerable to uncertainties than previous methods and we will have consistency checks between different detector components and an overlap with our previous CLAS measurements. Precise measurements of Gn M have already been made b...

It is shown that a relativistic particle has an upper limit of the mass and energy when it is accelerated to the speed of light. Now we can calculate the limiting parameters of the relativistic particles by the use of the normalized relativistic factor in Einstein's relativistic equations. For example, the maximum mass of the relativistic proton is a limited number of 1.1. 10 12 kg. The state of the relativistic particle is described by a mass balance and an energy balance. The energy balance includes the maximum energy of a relativistic particle and her real energy and her hidden energy.

Considering the model in which the effective interaction between any two quarks of a baryon can be approximately described by a simple harmonic potential, and making use of the expression of the energy obtained in Cartesian coordinates for the above mentioned model, we find a general expression for the radii of baryons. We then apply the expression to some baryons and find very consistent values for the radii of baryons and an experimental confirmation for the ground state of − Ξ .

Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, resulting in the several successful theorems of PCAC. On the other hand scalar confinement is suggested both by the spectroscopy of hadrons and by the string picture of confinement. However these two evidences are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we reformulate the coupling of the quarks to the string, and we are able to comply with chiral symmetry breaking, using scalar confinement. The results are quite encouraging. 1 Open Problem Recently Bjorken asked, " how are the many disparate methods of describing hadrons which are now in use related to each other and to the first principles of QCD?". Chiral symmetry breaking and scalar confinement are apparently conflicting, because chiral symmetry breaking requires a chiral invariant coupling to the quarks, say a vector coupling like in QCD. Here we try to solve this old conflict of hadronic physics, which remained open for many years. The QCD Lagrangian is chiral invariant in the limit of vanishing quark masses. This is crucial because Spontaneous chiral symmetry breaking is accepted to occur in low energy hadronic physics, for the light flavors u, d and s, where, mu, md << ms < Λ QCD < M N /3. The techniques of current algebra led to beautifully correct theorems, the PCAC (Partially Conserved Axial Current) theorems. The QM (Quark Models) are widely used as a simplification of QCD, convenient to study quark bound states and hadron scattering. Recently 1 we have shown that these beautiful PCAC theorems, like the Weinberg theorem for π − π scattering, are reproduced by quark models with spontaneous chiral symmetry breaking. On the other hand the confining potential for constituent quarks is probably scalar. Scalar confinement is suggested both by the spectroscopy of hadrons, by lattice simulations and by the string picture of confinement. In a pertubative QCD scenario, the hadron spectroscopy would be qualitatively similar to electronic spectra of the lighter atoms. It is remarkable that the Spin-Orbit potential (also called fine interaction in atomic physics) turns out to be suppressed in hadronic spectra because it is smaller than the Spin-Spin potential (also called hyperfine interaction). This constitutes an evidence of non-pertubative QCD. Another evidence of nonpertubative QCD is present in the angular and radial excitations of hadrons, which fit linear trajectories in Regge plots, and suggest a long range, probably linear, confining potential for the quarks. This led Henriques, Kellet and Moorhouse, Isgur and Karl, and others 2,3 to develop a Quark Model where a short-range vector potential plus a long-range scalar potential partly cancel

We present results on the electroexcitation of the low mass resonances ∆(1232)P33, N (1440)P11, N (1520)D13, and N (1535)S11 in a wide range of Q 2. The results were obtained in the comprehensive analysis of JLab-CLAS data on differential cross sections, longitudinally polarized beam asymmetries, and longitudinal target and beam-target asymmetries for π electroproduction off the proton. The data were analysed using two conceptually different approaches, fixed-t dispersion relations and a unitary isobar model, allowing us to draw conclusions on the model sensitivity of the obtained electrocoupling amplitudes. The amplitudes for the ∆(1232)P33 show the importance of a mesoncloud contribution to quantitatively explain the magnetic dipole strength, as well as the electric and scalar quadrupole transitions. They do not show any tendency of approaching the pQCD regime for Q 2 ≤ 6 GeV 2. For the Roper resonance, N (1440)P11, the data provide strong evidence for this state as a predominantly radial excitation of a 3-quark ground state. Measured in pion electroproduction, the transverse helicity amplitude for the N (1535)S11 allowed us to obtain the branching ratios of this state to the πN and ηN channels via comparison to the results extracted from η electroproduction. The extensive CLAS data also enabled the extraction of the γ * p → N (1520)D13 and N (1535)S11 longitudinal helicity amplitudes with good precision. For the N (1535)S11, these results became a challenge for quark models, and may be indicative of large meson-cloud contributions or of representations of this state different from a 3q excitation. The transverse amplitudes for the N (1520)D13 clearly show the rapid changeover from helicity-3/2 dominance at the real photon point to helicity-1/2 dominance at Q 2 > 1 GeV 2 , confirming a long-standing prediction of the constituent quark model.

We present results on the electroexcitation of the low mass resonances ∆(1232)P33, N (1440)P11, N (1520)D13, and N (1535)S11 in a wide range of Q 2. The results were obtained in the comprehensive analysis of JLab-CLAS data on differential cross sections, longitudinally polarized beam asymmetries, and longitudinal target and beam-target asymmetries for π electroproduction off the proton. The data were analysed using two conceptually different approaches, fixed-t dispersion relations and a unitary isobar model, allowing us to draw conclusions on the model sensitivity of the obtained electrocoupling amplitudes. The amplitudes for the ∆(1232)P33 show the importance of a mesoncloud contribution to quantitatively explain the magnetic dipole strength, as well as the electric and scalar quadrupole transitions. They do not show any tendency of approaching the pQCD regime for Q 2 ≤ 6 GeV 2. For the Roper resonance, N (1440)P11, the data provide strong evidence for this state as a predominantly radial excitation of a 3-quark ground state. Measured in pion electroproduction, the transverse helicity amplitude for the N (1535)S11 allowed us to obtain the branching ratios of this state to the πN and ηN channels via comparison to the results extracted from η electroproduction. The extensive CLAS data also enabled the extraction of the γ * p → N (1520)D13 and N (1535)S11 longitudinal helicity amplitudes with good precision. For the N (1535)S11, these results became a challenge for quark models, and may be indicative of large meson-cloud contributions or of representations of this state different from a 3q excitation. The transverse amplitudes for the N (1520)D13 clearly show the rapid changeover from helicity-3/2 dominance at the real photon point to helicity-1/2 dominance at Q 2 > 1 GeV 2 , confirming a long-standing prediction of the constituent quark model.

We present a relativistic chiral theory of nuclear matter which includes the effect of confinement. Nuclear binding is obtained with a chiral invariant scalar background field associated with the radial fluctuations of the chiral condensate Nuclear matter stability is ensured once the scalar response of the nucleon depending on the quark confinement mechanism is properly incorporated. All the parameters are fixed or constrained by hadron phenomenology and lattice data. A good description of nuclear saturation is reached, which includes the effect of in-medium pion loops. Asymmetry properties of nuclear matter are also well described once the full rho meson exchange and Fock terms are included.

Graphene, a two-dimensional crystal made of carbon atoms, provides a new and unexpected bridge between low and high-energy physics. The field has evolved very fast and very good reviews are already available in the literature. Graphene constitutes a condensed matter realization of lower dimensional quantum field theory models that were proposed to confront important-still unresolved-puzzles of the area: Chiral symmetry breaking and quark confinement. The new materials named topological insulators, closely related to graphene, are physical realizations of topological field theory. This article reviews some of these topics with the aim of bridging the gap and making these condensed matter issues accessible to high energy readers. The electronic interactions in the monolayer are analyzed with special emphasis on the recent experimental confirmation of some theoretical predictions. The issue of spontaneous chiral symmetry breaking in the model materials is also reviewed. Finally we give an extensive description of some recent topological aspects of graphene that allow to understand the main aspects of topological insulators.

Using the Nambu-Jona-Lasinio (NJL) model we study chemical potential response of the pion and kaon masses as a function of temperature and chemical potential, i.e., ∂m ∂µ (T , µ). First, we obtain the responses assuming the vector-axial vector coupling is zero (gV =0). Then, we include a non-zero gV and study the effects of gV on the responses. We find that the behavior of ∂m ∂µ for the pion is quite different from that for the kaon. It means that ∂m ∂µ is much dependent on the mass difference between the two quarks, i.e., the u and s quarks (or even between the u and d quarks). Our results may give a clue to future studies of ∂m ∂µ on the lattice. * In memory of Prof. Osamu Miyamura, a very kind and warm-hearted person as well as a great physicist.

A quiescent proton is a proton that is not involved in high-energy interactions. As is well known, the baryons in which the Proton is the most stable are described in the quantum mechanics system by a theory of quantum chromodynamics (QCD). QCD describes the details of interactions due to the scattering of protons with protons and other particles. In these energetic states, it works well. How is the internal structure of the proton described when it is in a passive state, not interacting energetically with other particles? In the passive or quiescent state, after years of effort, using QCD has not yielded a solution. The passive state is the subject of this paper. Protons, as well as neutrons, are the heaviest stable particles and are largely responsible for contributing mass that generates the global gravitation of the large Universe, leaving out dark matter and dark energy momentarily. This paper will explore how GR gravitation theory and the basic foundation of quantum mechanics, Planck Law, can describe the proton in the quiescent state. Due to the stability of the at-rest proton, this paper studies the proton in this quiet state. The Neutron is known to be stable when part of a more complex atomic nucleus but decays, when free, into a proton, electron, and electron-antineutrino. Due to this instability, neutrons will not be included in this study.

The study of superconductivity, dual superconductivity and color superconductivity has been undertaken through the breaking of super symmetric gauge theory in restricted chromo dynamics (RCD) which automatically incorporates the condensation of monopoles and dyons leading to confining and superconducting phases. Dyonic supermultiplets in N = 1 super symmetry have been obtained quantum mechanically in RCD and it has been shown that dyon appears in RCD theory only through restricted part of the generalized potential and it is only this part of this potential which is responsible for quark confinement and the resulting superconductivity through the mechanism of dyonic condensation.

Using renormalization group and field equation techniques and several smoothness assumptions, we argue the effective charge in an ultraviolet free SU (iV) color gauge theory becomes infinite in the infrared limit if the number of quark flavors exceeds 13N/4.

Recent lattice calculations performed at zero temperature and in the maximal center gauge indicate that quark confinement can be understood in this gauge as due to fluctuations in the number of magnetic vortices piercing a given Wilson loop. This development has led to a revival of the vortex condensation theory of confinement. For a SU(2) gauge group, we show that also at finite temperatures, center vortices are the relevant collective infrared degrees of freedom determining the long-range static quark potential; in particular, their dynamics reflect the transition to the deconfining phase.

Dark matter self-scattering is one of key ingredients for small-scale structure of the Universe, while dark matter annihilation is important for the indirect measurements. There is a strong correlation between the velocity-dependent self-scattering cross section and the Sommerfeld enhancement factor for the dark matter annihilation cross section. In this study, we formulate a direct relation between them by the use of Watson's (initial state/final state) theorem and Omnès solution, and our formulation reproduces the Sommerfeld enhancement factor, which directly computed by solving the Schrödinger equation, from the scattering phase shift.

In this paper an intrinsically non-Abelian black hole solution for the SU (2) Einstein-Yang-Mills theory in four dimensions is constructed. The gauge field of this solution has the form of a meron whereas the metric is the one of a Reissner-Nordström black hole in which, however, the coefficient of the 1/r 2 term is not an integration constant. Even if the stress-energy tensor of the Yang-Mills field is spherically symmetric, the field strength of the Yang-Mills field itself is not. A remarkable consequence of this fact, which allows to distinguish the present solution from essentially Abelian configurations, is the Jackiw, Rebbi, Hasenfratz, 't Hooft mechanism according to which excitations of bosonic fields moving in the background of a gauge field with this characteristic behave as Fermionic degrees of freedom.

A potential model for mesons is presented, which combines quark confinement and strong decay in a realistic approach. The multichannel Schrodinger formalism is employed to describe a system of one or more permanently closed quark-antiquark channels in interaction with several two-meson channels. For the potential in the qq channels a harmonic oscillator with constant frequency is taken. As for the meson channels only Okubo-Zweig-Iizuka-rule-allowed decays into two mesons of the pseudoscalar or vector type are considered. Final-state interactions between these mesons are not yet taken into account. The communication between confined and free channels is supposed to take place via the 'I'0 mechanism, for which a locally approximated transition potential is derived. In order to obtain an analytic solution for the S matrix, the transition potential is treated by using a multi-5-shell method. Kinematically relativistic corrections and color splitting allow a fairly successful treatment of pseudoscalar as well as vector mesons for all quark flavors. The results are confronted with the data and discussed.