Chiral Phase Transitions in QED at Finite Temperature : Dyson-Schwinger Equation Analysis in the Real Time Hard-Thermal-Loop Approximation(Particles and Fields)

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In order to clarify the essential thermal effects that govern the chiral phase transition at finite temperature, we investigate, in the real-time thermal QED, the consequences of the hard-thermal-loop (HTL) resummed Dyson-Schwinger equation for the physical fermion mass function Σ_R. Since Σ_R is the mass function of an "unstable" quasi-particle in thermal field theories, it necessarily has non-trivial imaginary parts, together with non-trivial wave function renormalization constants. Analyses so far have completely disregarded this fact, despite it being one of the basic outcomes of thermal field theory. The "approximation", which ignores the imaginary parts of Σ_R, gives (non-trivial) constraint equations to be solved simultaneously. For this reason, this approximation cannot be applied consistently except in the trivial case, Σ_R=0. In the present analysis we correctly take this fact into account, and study, in the ladder approximation, the effect of the HTL resummed gauge boson propagator. Our results obtained using numerical analysis, reveal two facts: i) the chiral phase transition is of second order, since the fermion mass is dynamically generated at a critical value of the temperature T_c, or at a critical coupling constant α_c, without any discontinuity; and ii) the critical temperature T_c at a fixed value of α is significantly lower than that obtained previously, which means that the restoration of chiral symmetry occurs at a lower temperature than previously expected. The second fact shows the importance of correctly incorporating the essential thermal effect into the analysis of the chiral phase transition. A procedure for taking account of the gauge invariance in the present approximation is also discussed.
理論物理学刊行会の論文
2003-10-25

Chiral Phase Transitions in QED at Finite Temperature : Dyson-Schwinger Equation Analysis in the Real Time Hard-Thermal-Loop Approximation(Particles and Fields)

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