On path integral localization and the Laplacian, the thesis

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dc.creatorKärki, Topi
dc.date1999-05-27
dc.date.accessioned2026-07-07T04:32:49Z
dc.date.available2026-07-07T04:32:49Z
dc.descriptionIn this thesis, we develop path integral localization methods that are familiar from topological field theory: the integral over the infinite dimensional integration domain depends only on local data around some finite dimensional subdomain. We introduce a new localization principle that unifies BRST localization, the non-Abelian localization principle and the conformal generalization of the Duistermaat-Heckman integration formula. In addition, it is studied if one can possibly derive a generalized Selberg's trace formula on locally homogeneous manifolds using localization techniques. However, a definite answer is obtained only in the Lie group case (we complete the work of R. Picken) in which it is an application of the Duistermaat-Heckman integration formula. Also a new derivation of DeWitt's term is reported. Furthermore, connections between evolution operators of integrable models and localization methods are studied. A derivative expansion localization is presented and it is conjectured to apply also to integrable models, for example the Toda lattice. Moreover, a pedagogical introduction to the localization techniques is given, as well as a list of selected references that might be useful for a beginning graduate student in mathematical physics or for a mathematician who would like to study the physical point of view to topological field theory and string theory.
dc.description40 pages, uses antero.sty that is included, Ph.D. thesis, Uppsala University
dc.identifierhttps://arxiv.org/abs/math-ph/9905021
dc.identifierhttp://arxiv.org/abs/math-ph/9905021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58338
dc.subjectMathematical Physics
dc.subject53Z05
dc.titleOn path integral localization and the Laplacian, the thesis
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