'Variational' optimization in quantum field theory

We examine two different techniques for studying quantum field theories in which a 'variational' optimization of parameters plays a crucial role. In the context of the O(N)-symmetric $\lambda\phi\sp4$ theory we discuss variational calculations of the effective potential that go beyond the Gaussian approximation. Trial wavefunctionals are constructed by applying a unitary operator U = e\sp{-isπ\sb{R}\phi\sbsp{T}{2}} to a Gaussian state. We calculate the expectation value of the Hamiltonian using the non-Gaussian trial states generated, and thus obtain optimization equations for the variational-parameter functions of the ansatz. At the origin, $\varphi\sb{c} = 0,$ these equations can be solved explicitly and lead to a nontrivial correction to the mass renormalization, with respect to the Gaussian case. Numerical results are obtained for the (0 + 1)-dimensional case and show a worthwhile quantitative improvement over the Gaussian approximation. We also discuss the use of optimized perturbation theory (OPT) as applied to the third-order quantum chromodynamics (QCD) corrections to $R\sb{e\sp+e\sp-}.$ The OPT method, based on the principle of minimal sensitivity, finds an effective coupling constant that remains finite down to zero energy. This allows us to apply the Poggio-Quinn-Weinberg smearing method down to energies below 1 GeV, where we find good agreement between theory and experiment. The couplant freezes to a zero-energy value of α\sb{s}/π = 0.26, which is in remarkable concordance with values obtained phenomenologically.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Natural Sciences

Grantor

Rice University

Year dc:date.issued

1993

Author dc:creator

• Mattingly, Alan Charles

Advisor dc:contributor.advisor

• Stevenson, Paul M.

• Elementary particles
• High energy physics
• Particle physics

Statement dc:rights

• Copyright 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.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/16649

OAI identifier oai:identifier

oai:repository.rice.edu:1911/16649