Second-order corrections to the Gaussian effective potential for lambda phi(4) and other theories

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dc.contributor.advisorStevenson, Paul M.en_US
dc.creatorStancu, Ionen_US
dc.date.accessioned2009-06-04T00:11:56Zen_US
dc.date.available2009-06-04T00:11:56Zen_US
dc.date.issued1990en_US
dc.description.abstractWe formulate a systematic, nonperturbative expansion for the effective potential of $\lambda\phi\sp4$ theory. At first order it gives the Gaussian effective potential (GEP), which itself contains the 1-loop and leading-order $1\over N$ results. Here, we compute the second-order terms and hence obtain the post-Gaussian effective potential (PGEP) in 1, 2, 3, and 4 spacetime dimensions. The renormalization procedure, including the calculation of the physical mass, is discussed in detail. The results in lower dimensions agree well with the GEP when the comparison is made for the same values of the bare parameters. In 4 dimensions the divergent integrals are calculated using coordinate-space methods combined with dimensional regularization. (Difficulties with other regularizations are briefly discussed). The PGEP for the "precarious" $\lambda\phi\sp4$ theory is obtained in manifestly finite form. Remarkably, the final result takes the same mathematical form as the GEP, with only some numerical co-efficients being changed. Indeed, when parametrized in terms of the physical mass and the renormalized coupling constant, only a single coefficient is changed, from 1 to 1-1/(N + 3)$\sp2$. The "autonomous" version of the 4-dimensional theory refuses to work in this approach: one obtains indeed an autonomous-like theory, but it is unbounded below for a certain range of the parameters. The influence of fermions on scalar systems is also investigated in the post-Gaussian approximation. For the simple case of an Yukawa-type coupling with no scalar self-interaction terms the results turn out to be the same as in the Gaussian approximation.en_US
dc.format.extent126 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoThesis Phys. 1990 Stancuen_US
dc.identifier.citationStancu, Ion. "Second-order corrections to the Gaussian effective potential for lambda phi(4) and other theories." (1990) Diss., Rice University. <a href="https://hdl.handle.net/1911/16394">https://hdl.handle.net/1911/16394</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16394en_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.subjectParticle physicsen_US
dc.subjectElementary particlesen_US
dc.subjectHigh energy physicsen_US
dc.titleSecond-order corrections to the Gaussian effective potential for lambda phi(4) and other theoriesen_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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