Fermion Determinant with Dynamical Chiral Symmetry Breaking

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

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.     

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.     

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...     

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.     

Dynamical Chiral Symmetry Breaking and Phase Transition of Cuprate Superconductors in QED3

With the coupled Dyson-Schwinger equations in the framework of the unified QED₃ theory, we study the phase transition between the antiferromagnet(AF) and the d-wave superconductor (dSC) of planar cuprates at T=0. By solving the coupled Dyson-Schwinger equations both analytically and numerically in rainbow approximation in Landau gauge and comparing the obtained results with that given in the 1/N expansion, we find that there exists a chiral symmetry breaking from dSC phase to AF phase when the quasi-fermion flavors N≤4 in half-filling and the AF phase can possibly coexist with the dSC phase in the underdoped region. By comparing the pressure between the coexistent AF-dSC phase and dSC phase, we find that AF-dSC coexisting phase is the stable phase, the AF phase can then coexist with the dSC phase.     

Topological Approach to the Study of Dynamical Symmetry Breaking in IBM System

The process of the dynamical symmetry breaking in nuclear IBM system is studied by using the topological approach and laying stress on the singular behavior and origin of the energy levels of avoided crossing.It is shown that avoided crossing is really due to unstable fixed point of the dynamical mapping.Beyond such point,to perform the continuous mapping requires a localized permutation of the two levels concerned,and the mapping can no longer be expressible by the generators of the dynamical group.Thus,dynamical symmetry is localized and essentially destroyed.     

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.     

Chiral Soliton Model with Dynamical Restoration of Chiral Symmetry from Quark Flavour Dynamics

The Nambu-Jona-Lasinio model as a particular model of quark flavour dynamics is bosonized in the low-energy regime using a generalized heat kernel expansion with local mass scale. The resulting effective meson Lagrangian defines a chiral soliton model, the solutions of which show a partial restoration of chiral symmetry inside the soliton.     

The Quarkonium Potential Within the Short and Intermediate Range in QCD

A quark-antiquark potential is calculated by involving vacuum condensates up to dimension-6 in QCD in the background fields. The underlying assumption is that a gluon (quark) propagates, not in the empty space, but through the physics vacuum, filled with the background fields. The interactions of the gluon with the background fidds manifest themselves as the corrections of vacuum condensates to the free gluon propagator. It is shown that these corrections extend the potential from the short distances to the intermediate range. Indeed, with some reasonable parameters, the resulting potential is similar to those popular phenomenological potentials in shape in the region of 0.1 < γ < 1 fm.     

Chiral Symmetry Breaking for Fermions Charged under Large Lie Groups

We reexamine the dynamical generation of mass for fermions charged under various Lie groups with equal charge and mass at a high Grand Unification scale, extending the Renormalization Group Equations in the perturbative regime to two loops and matching to the Dyson-Schwinger Equations in the strong coupling regime.     

Dynamical Symmetry Breaking for Weinberg-Salam Model and Restoration at Finite Temperature

In this paper, we utilize Nambu-Jona-Lasinio (NJL) mechanism to discuss the dynamical symmetry breaking for Weinberg-Salam model. In the NJL mechanism the symmetry breaking not only is determined by the potential ofscalar field V(φ) but also has important relation with condensate of the fermion pair (φφ). We find that the coefficient of quadric term of scalar field μ² ≥ 0 can still cause symmetry breaking by virtue of (φφ) ≠ 0, and the vacuum expected value of scalar field obeys (φ) = (φφ), i.e., the order parameter which causes phase transition is the condensate of fermion pair (φφ). We also discuss the restoration problem of SU(2) × U(1) gauge symmetry breaking by the NJL mechanism at high temperatures.     

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.     

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.     

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.     

Density-Dependence of Nuclear Symmetry Energy: Role of QCD Chiral Phase Transition

The density-dependence of symmetry energy is of particular importance to many problems in nuclear physics and astrophysics. By using the functional path integral method, we show explicitly the relation between nuclear symmetry energy and isospin susceptibility. The latter one is found to be a probe to the QCD chiral phase transition. We further found in the Nambu-Jona-Lasinio model calculations that, the nuclear symmetry energy has an abrupt change at the critical nuclear density where the chiral symmetry restores partially.     

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.     

Calculation of Quark Condensate in Nuclear Matter with the Chiral Symmetry Spontaneous Breaking Lagrangian

Using the chiral symmetry spontaneous breaking Lagrangian with mean-field approximation, we investigate the in-medium quark condensate 〈qq〉. It is found that the condensate decreases as the nuclear matter density ρ increases. Meanwhile, the desent deviates from the linear decrease and becomes remarkably slow as the density of the nuclear matter further increases. It shows that the chiral symmetry spontaneous breaking is only partially restored in densed nuclear matter.