Abstract
The optimized expansion for the path integral representation of the generating functional in quantum field theory is formulated. The first-order effective action is obtained in scalar and fermion field theories with quartic self-interactions. To this approximation the scalar theory is renormalized in the space-time dimension n = 4 and 5, and the fermion theory in n = 2 and 3. Thermal properties of the renormalized theories are studied by means of the finite-temperature effective potential. Both theories appear trivial or precarious
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