| Abstract
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The Gaussian effective potential (GEP), a non-perturbative approach to study quantum field theory, is applied to scalar and scalar-fermion models. We study the scalar usd\phi\sp6usd field coupled to fermions through g{\rm B}\phi\overline{\psi}\psi or g{\rm B}\phi\sp2\overline{\psi}\psi in 2 and 3 space-time dimensions. In addition, we derive the finite temperature (T > 0) GEP from first principles and apply it to study these models at T > 0. Also the Autonomous usd\lambda\phi\sp4usd, coupled to fermions through a Yukawa term (g{\rm B}\phi\overline{\psi}\psi), is examined in 4 dimensions at T > 0. In all these models, in order to obtain stable theories, it is found that gB must vanish as 1/log(Muv), 1/Muv or 1/Msp{\rm uv}{2} in 2, 3 or 4 dimensions respectively, Muv being an ultraviolet cutoff which is sent to infinity. The contribution of fermions to the GEP, however, is nonvanishing. It is also found that for the class of theories discussed, symmetry, if broken, is restored above a critical temperature. The coupling constant parameter space for each model is studied carefully, and regions where symmetry breaking occurs are determined both at zero and finite temperature.
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