Abstract
The optimized expansion for the generating functional for Green's functions in the path-integral representation is formulated in quantum field theory of fermions with a scalar Fermi interaction and compared with different expansion techniques. The effective action in n-dimensional space-time is calculated to the first order. Renormalization can be performed if the space-time dimension is less than four. In this case, the renormalized effective potential at a finite temperature is calculated to first order. The results suggest that the theory in two- and three-dimensional space-time is noninteracting or precarious.
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