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Based on a general analysis of Green functions in the real-time thermal field theory, we have proven that the four-point amputated functions in a NJL model in the fermion bubble diagram approximation behave like usual two-point functions. We expound the thermal transformations of the matrix propagator for a scalar bound state in the $F\bar{F}$ basis and in the $RA$ basis. The resulting physical causal, advanced and retarded propagator are respectively identical to corresponding ones derived in the imaginary-time formalism and this shows once again complete equivalence of the two formalisms of thermal field theory on the discussed problem in the NJL model.

communications in theoretical physics/communications in theoretical physics

Two-Point Function Reduction of Four-Point Amputated Functions and Transformations in $F\bar{F}$ and <i>RA</i> Basis in a Real-Time Finite Temperature NJL Model

Two-Point Function Reduction of Four-Point Amputated Functions and Transformations in $F\bar{F}$ and RA Basis in a Real-Time Finite Temperature NJL Model