By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynami...By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.展开更多
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...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 A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot 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.展开更多
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 ...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, and approximately for Quantum Chromodynamics, 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 an 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.展开更多
By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the criti...By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μ<SUB>c</SUB> in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μ<SUB>c</SUB> 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 in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.展开更多
We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion inte...We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interactionmodels. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicitexpressions for the effective potentials at zero temperature in the cases of D = 2,3, and 4 for practical use.展开更多
文摘By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in D = 2 and D = 3 Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some specJal first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in D = 3 GN model a first order phase transition does occur in the case of zero temperature and finite chemical potential.
文摘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 A/m(0), the ratio of the momentum cutoff A in the fermion-loop integrals to the dynamicalfermion mass m(0) at zero temperature, is less than 3.387 or not. The former condition cannot 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.
文摘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, and approximately for Quantum Chromodynamics, 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 an 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.
基金The project supported by National Natural Science Foundation ot China
文摘By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μ<SUB>c</SUB> in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μ<SUB>c</SUB> 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 in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.
文摘We have proven the general relations between the gap equations obeyed by dynamical fermion mass and thecorresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interactionmodels. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicitexpressions for the effective potentials at zero temperature in the cases of D = 2,3, and 4 for practical use.
