1999/05/27 by Topi Kärki, Kärki, Topi
Mathematics · Physics and Astronomy · #53Z05 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:53Z05
paper · pdf · doi:10.48550/arxiv.math-ph/9905021
40 pages, uses antero.sty that is included, Ph.D. thesis, Uppsala University
arxiv created 1999/05/27 · arxiv updated 2009/11/30
In 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.