The temporal axial gauge at finite temperature explored using the real time formalism

1990 ◽  
Vol 48 (1) ◽  
pp. 169-182 ◽  
Author(s):  
K. A. James
Keyword(s):  
Real Time ◽  
Finite Temperature ◽  
The Real ◽  
Axial Gauge ◽  
Time Formalism ◽  
Real Time Formalism

scholarly journals FINITE-TEMPERATURE AND FINITE-DENSITY QED: THE SCHWINGER-DYSON EQUATION IN THE REAL-TIME FORMALISM

1995 ◽  
Vol 10 (02) ◽  
pp. 199-232 ◽  
Author(s):  
KEI-ICHI KONDO ◽  
KAZUHIRO YOSHIDA
Keyword(s):  
Real Time ◽  
Finite Temperature ◽  
Dyson Equation ◽  
Temperature Phase ◽  
Continuous Variables ◽  
Imaginary Time ◽  
Gap Equation ◽  
The Real ◽  
Time Formalism ◽  
Real Time Formalism

We derive, based on the real-time formalism (especially thermo-field-dynamics), the Schwinger-Dyson gap equation for the fermion propagator in QED and the four-fermion model at finite temperature and density. We discuss some advantages of the real-time formalism in solving the self-consistent gap equation, in comparison with the ordinary imaginary-time formalism. Once we specify the vertex function, we can write down the SD equation with only continuous variables without performing the discrete sum over Matsubara frequencies which cannot be performed in advance without further approximation in the imaginary-time formalism. By solving the SD equation obtained in this way, we find the chiral-symmetry-restoring transition at finite temperature and present the associated phase diagram of strong-coupling QED. In solving the SD equation, we consider two approximations: instantaneous-exchange and p0-independent ones. The former has a direct correspondence in the imaginary-time formalism; the latter is a new approximation beyond the former, since it is able to incorporate new thermal effects which have been overlooked in the ordinary imaginary-time solution. However, the two approximations are shown to give qualitatively the same results on the finite-temperature phase transition.

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