Fermion Self-Energy and Chiral Symmetry Breaking from Four-Fermion and Gauge Interactions

The exact analytic solutions of the linearized Schwinger-Dyson equation of fermion self-energy are used to obtain the effective four-fermion and gauge coupling criticality curves for dynamical chiral symmetry breaking. The results show that when the zero-momentum gauge coupling a(0) < a₀(0), the critical gauge coupling in the pure gauge interaction case, the minimal critical four-fermion coupling β_min is always nonzero and positive and will go up as the a(0) decreases. The use of the exact solutions also allows us to make quite definite estimations of the momentum scales where chiral symmetry breaking would happen if the values of an infrared parameter ξ are given separately.     

Physical Gauge in the Problem of Dynamical Chiral Symmetry Breaking in QED in a Magnetic Field

We describe how the choice of an appropriate (physical) gauge leads to the solution of a nonperturbative problem in quantum electrodynamics: dynamical chiral symmetry breaking in QED in a constant magnetic field.     

Light Quark Masses in the Theory with the Dynamical Breaking of Chiral Symmetry

JETP Letters - Mass formulas and decay constants of pseudoscalar π and K mesons have been obtained in the theory with four-quark interactions. To calculate the quark determinant, a Volterra...     

Fermion Determinant with Dynamical Chiral Symmetry Breaking

One-loop fermion determinant is discussed for the case in which the dynamical chiral symmetry breaking caused by momentum-dependent fermion self-energy Σ(p²) takes place. The obtained series generalizes the heat kernel expansion for hard fermion mass.     

A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A generalized Yang-Mills model, which contains, besides the vector part V_μ, also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry

A maximally generalized Yang-Mills model, which contains, besides the vector part V_μ, also an axial-vector part A_μ, a scalar part S, a pseudoscalar part P, and a tensor part T_μν, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of thevertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Gauge Symmetry and Transverse Symmetry Transformations in Gauge Theories

The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD （Quantum Chromodynamics） leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of the vertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.     

Chiral Syqmetry Restoration in Lattice Gauge Theory

The pion mass& calculated starting from the strongly coupling effective Hamiltonian for Wilson fermions by using Green function method. The possibility of the chiral symmetry restoration at a critical quark maas is also investigated.     

The Effect of Spontaneous Breaking of Gauge Symmetry in Cosmology with Rotation

The effect of spontaneous breaking of gauge symmetry is studied for cosmological models with expansion and rotation with the Bianchi metrics of types II, IV, V, and VI. The conditions are defined wherein the effect is manifested in these models.     

Chiral Symmetry Breaking and Confinement in Minkowski Space QED2+1

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e.g. with the standard Euclidean calculation.     

Intermediate Range Force Contributions to Dynamical Chiral Symmetry Breaking in QCD

We propoee the intermediate range QCD force singular like δ(q) by analysing the gluon propagator in the nonperturbative region from QCD sum rules. With the help of the Slavnov- Taylor-Ward identity we derive the equations for the nonperturbative quark propagator from the Schwinger-Dyson (SD) equation. Solutione for the quark propagator in two special cases are given. We find that the intermediate range force L also responsible for the chiral symmetry breaking in QCD.     

手征对称性动力学破缺和铜氧化物超导体相变的三维量子电动力学研究

利用三维量子电动力学理论中的Dyson-Schwinger方程方法, 研究了零温情况下平面铜氧化合物超导体的反铁磁相和d波超导相之间的相变. 通过在朗道规范下近似解析求解和数值求解完全耦合的Dyson-Schwinger方程、并将所得结果与1/N展开方法的结果相比较, 发现在半填充准费密子味道数约小于等于4的情况下, 通过手征对称性自发破缺, d波超导相可以演化到反铁磁相, 并且反铁磁相有可能与d波超导相共存. 通过进一步比较不同相的压强, 还说明反铁磁与d波超导共存相为稳定相, 从而反铁磁相确实可以与d波超导相共存.     

On the Dimensions of the Chiral and Dilatation Symmetry Breaking Hamiltonian Densities

Denoting by l_u and l_δ the dimensions (if any) of the chiral and dilation symmetry breaking Hamiltonian densities u(x) and δ(x), respectively, the property (4 – l_u) (l_u – l_δ) > 0 (which is already known in special cases) is derived for a much larger class of models. We furthermore obtain a simple and general explicit expression for u(x) in terms of the current divergences, and review the physical applications of this (or an analogous, almost obvious) expression.     

Chiral Symmetry Breaking as a Phase Transition in QED Plus NJL Model

The chiral symmetry breaking (CSB) of massless &ED is studied analytically and then numerically by introducing a Nambu-Jona-Lasinio (NJL) term. We use the method of relativistic canonical transformation and random phase approximation to find the criterion for CSB (i.e., the condensation in vacuum) and the accompanying elementary excitations. The role played by NJL term, the scale anomaly and the meaning of critical point (α_c≈1.5) are discussed.     

Restoration of Chiral Symmetry in Light-Front Finite-Temperature Field Theory

We investigate the properties of qq and states in hot and dense quark matter in the framework of light-front finite-temperature field theory. Presently we use the Nambu–Jona-Lasinio model of QCD and derive the gap equation at finite temperature and density. We study pionic and scalar diquark dynamics in quark matter and calculate the masses and the Mott dissociation as a function of the temperature T and the chemical potential μ. For the scalar diquark we determine the critical temperature of color superconductivity.     

Mass and spin of Poincaré Gauge Theory

We discuss two expressions for the conserved quantities (energy momentum and angular momentum) of the Poincaré Gauge Theory. We show, that the variations of the Hamiltonians, of which the expressions are the respective boundary terms, are well defined, if we choose an appropriate phase space for asymptotic flat gravitating systems. Furthermore, we compare the expressions with others, known from the literature.     

Vacuum Radiation and Symmetry Breaking in Conformally Invariant Quantum Field Theory

The underlying reasons for the difficulty of unitarily implementing the whole conformal group SO(4,2) in a massless Quantum Field Theory (QFT) on Minkowski space are investigated in this paper. Firstly, we demonstrate that the singular action of the subgroup of special conformal transformations (SCT), on the standard Minkowski space $M$, cannot be primarily associated with the vacuum radiation problems, the reason being more profound and related to the dynamical breakdown of part of the conformal symmetry (the SCT subgroup, to be more precise) when representations of null mass are selected inside the representations of the whole conformal group. Then we show how the vacuum of the massless QFT radiates under the action of SCT (usually interpreted as transitions to a uniformly accelerated frame) and we calculate exactly the spectrum of the outgoing particles, which proves to be a generalization of the Planckian one, this recovered as a given limit. Received: 17 September 1997 / Accepted: 7 July 1998