Stevenson, Paul M.2009-06-042009-06-041988Hajj, George Antoine. "Nonperturbative studies of scalar and scalar-fermion quantum field theories at zero and finite temperature using the Gaussian effective potential." (1988) Diss., Rice University. <a href="https://hdl.handle.net/1911/16147">https://hdl.handle.net/1911/16147</a>.https://hdl.handle.net/1911/16147The 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 $\phi\sp6$ field coupled to fermions through g$\sb{\rm B}\phi\overline{\psi}\psi$ or g$\sb{\rm B}\phi\sp2\overline{\psi}\psi$ 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 $\lambda\phi\sp4$, coupled to fermions through a Yukawa term (g$\sb{\rm B}\phi\overline{\psi}\psi$), is examined in 4 dimensions at T $>$ 0. In all these models, in order to obtain stable theories, it is found that g$\sb{\rm B}$ must vanish as 1/log(M$\sb{\rm uv}$), 1/M$\sb{\rm uv}$ or 1/M$\sbsp{\rm uv}{2}$ in 2, 3 or 4 dimensions respectively, M$\sb{\rm uv}$ 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.159 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Particle physicsElementary particlesHigh energy physicsThesisThesis Phys. 1988 Hajj