arXiv subjects

Zhou Bang-Rong

Publications and source records attributed to Zhou Bang-Rong.

9 recordsLinked to original sources

arXiv2007

Quark-Antiquark and Diquark Condensates in Vacuum in a 2D Two-Flavor Gross-Neveu Model

The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio (NJL) model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark condensates in vacuum also depends on $G_S/H_S$, the ratio of the coupling constants in scalar quark-antiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if $G_S/H_S>2/3$ which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if $0<G_S/H_S<2/3$. However, different from the 4D NJL model, the pure diquark condensates arise only at $G_S/H_S=0$ and are not in a possibly finite region of $G_S/H_S$ below 2/3.

hep-th↗

arXiv2005

Real-Time thermal Ward-Takahashi Identity for vectorial current in QED and QCD

It is shown that, by means of canonical operator approach, the Ward-Takahashi identity (WTI) at finite temperature $T$ and finite chemical potential $μ$ for complete vectorial vertex and complete fermion propagator can be simply proven, rigorously for Quantum Electrodynamics (QED) and approximately for Quantum Chromodynamics (QCD) where the ghost effect in the fermion sector is neglected. The WTI shown in the real-time thermal matrix form will give definite thermal constraints on the imaginary part of inverse complete Feynman propagator including self-energy for fermion and will play important role in relevant physical processes. When the above inverse propagator is assumed to be real, the thermal WTI will essentially be reduced to its form at $T=μ=0$ thus one can use it in the latter's form. At this point, a practical example is indicated.

hep-th↗

arXiv2005

Real-time thermal Schwinger-Dyson equation for quark self-energy in Landau gauge

By means of a formal expression of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by $A(p^2)\not{p}-B(p^2)$, we argue that, when temperature $T$ is less than the given infrared momentum cutoff $p_c$, $A(p^2)=1$ is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.

hep-th↗

arXiv2005

Cornwall-Jackiw-Tomboulis effective potential for quark propagator in real-time thermal field theory and Landau gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function $A(p^2)$ in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential which will be a useful means to research chiral phase transition in QCD in the real-time formalism.

hep-th↗

arXiv2003

Symmetry restoring phase transitions at high density in a 4D Nambu-Jona-Lasinio model with a single order parameter

High density phase transitions in a 4 dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second order at a high temperature $T$; however at T=0, they are first- or second- order, depending on whether $Λ/m(0)$, the ratio of the momentum cutoff $Λ$ in the fermion loop integrals to the dynamical fermion mass $m(0)$ at zero temperature, is less than 3.387 or not. The former condition can not be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.

hep-th↗

arXiv2003

Particle density in zero temperature symmetry restoring phase transitions in four-fermion interaction models

By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we have shown by explicit calculations that when T=0 the particle density will have a discontinuous jumping across the critical chemical potential $μ_c$ in 2D and 3D Gross-Neveu (GN) model and these physically explain the first order feature of corresponding symmetry restoring phase transitions. For second order phase transitions in 3D GN model when $T\to 0$ and in 4D Nambu-Jona-Lasinio (NJL) model when T=0, it has been proven that the particle density itself will be continuous across $μ_c$ but its derivative over the chemical potential $μ$ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point $(T,μ)=(0,μ_c)$ in 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.

hep-th↗

arXiv2003

Second and first order phase transition in three dimension Gross-Neveu model

Symmetry restoring phase transitions in three dimension Gross-Neveu model are shown to be second order at finite temperature $T$ and first order at T=0 and finite chemical potential $μ$ by critical analysis of the dynamical fermion mass based on the gap equation. The latter is further verified by effective potential analysis. The resulting tricritical point is $(T,μ)=(0,m(0))$, where $m(0)$ is the dynamical fermion mass at $T=μ=0$. Physical difference between the above second and first order phase transition is illustrated by means of variations of thermodynamical particle density.

hep-th↗

arXiv2003

Gap equations and effective potentials at finite temperature and chemical potential in D dimensional four-fermion models

We have proven the general relations between the gap equations obeyed by dynamical fermion mass and corresponding effective potentials at finite temperature and chemical potential in D dimensional four-fermion interaction models. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicit expressions for the effective potentials at zero temperature in the cases of $D=2,3$ and 4 for practical use.

hep-ph↗

arXiv2002

Real-time thermal field theory analyses of 2D Gross-Neveu model

Discrete symmetry breaking and possible restoration at finite temperature $T$ are analysed in 2D Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass $m$ is proven to be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the mean field approximation used in the auxialiary scalar field approach. Reproducing of the non-zero critical temperature $T_c=0.567 m(0)$, ($m(0)$ is the dynamical fermion mass at T=0), shows the equivalence between the real-time and the imaginary-time thermal field theory in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the $\ln(T_c/T)$ behavior of $m^2$ at $T\stackrel{<}{\sim} T_c$ can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.

hep-th↗