Bogolubov's chain of equations method for temperature Wightman functions in thermodynamics of relativistic phase transition

TL;DR

This paper applies Bogolubov's chain of equations to analyze temperature Wightman functions in relativistic phase transitions, deriving equations for effective masses and thermodynamic properties, with corrections found to be small except near phase equilibrium.

Contribution

It introduces a detailed application of Bogolubov's chain method to relativistic phase transitions, including derivation of equations for effective masses and thermodynamic quantities.

Findings

Effective masses and order parameters derived from the chain equations.

Thermodynamic quantities like heat capacity and sonic speed calculated.

Corrections to the Hartree-Fock approximation are small except near phase equilibrium.

Abstract

Bogolubov's chain of equations method for temperature Wightman functions is suggested for investigation of relativistic phase transition. The chain equations for the Wightman functions forming momentum--energy tensor are obtained. It is clarified that structure of the chain equations determines the basis approximation (the Hartree - Fock approximation) and corrections calculation algorithm. The basis approximation is investigated in details: renormalized equations for effective masses, order parameter and generating functional which reproduce those equations are obtained. Being considered on the solution of the gap equations for the effective masses the generating functional turns to nonequilibrium functional of free energy density, which allows to obtain phases stability conditions. Thermodynamic observables like heat capacity and sonic speed are calculated. The correction to the Hartree-Fock approximations is ascertained to be small for all temperatures excluding vicinity of the phases equilibrium point.