'Variational' optimization in quantum field theory

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dc.contributor.advisorStevenson, Paul M.en_US
dc.creatorMattingly, Alan Charlesen_US
dc.date.accessioned2009-06-04T00:34:54Zen_US
dc.date.available2009-06-04T00:34:54Zen_US
dc.date.issued1993en_US
dc.description.abstractWe 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 $U = e\sp{-is\pi\sb{R}\phi\sbsp{T}{2}}$ 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 $\alpha\sb{s}/\pi = 0.26,$ which is in remarkable concordance with values obtained phenomenologically.en_US
dc.format.extent90 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoThesis Phys. 1993 Mattinglyen_US
dc.identifier.citationMattingly, Alan Charles. "'Variational' optimization in quantum field theory." (1993) Diss., Rice University. <a href="https://hdl.handle.net/1911/16649">https://hdl.handle.net/1911/16649</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16649en_US
dc.language.isoengen_US
dc.rightsCopyright 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.en_US
dc.subjectElementary particlesen_US
dc.subjectHigh energy physicsen_US
dc.subjectParticle physicsen_US
dc.title'Variational' optimization in quantum field theoryen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentPhysicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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