Type
Text
Type
Dissertation
Advisor
Khuri, Marcus | Movshev, Mikhail | Viro, Oleg | Abanov, Alexander.
Date
2015-12-01
Keywords
Mathematics | loop space, mass gap, regularized geometry, sigma model
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76397
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Interest in nonlinear sigma models with target space a symmetric space of positive curvature comes from both mathematics and physics. In this dissertation we focus on the two-dimensional nonlinear sigma model with target space the k-dimensional projective space P^k. We study the properties of a finite-dimensional approximation, which we denote by L_N(P^k), to the loop space L(P^k), and construct resolutions of singularities for these truncated loop spaces. We also look into the geometries of such spaces and propose a conjecture about the mass gap of the Schrodinger operator H on L_N(P^k) with analytic formula. | 55 pages
Recommended Citation
Hao, Cheng, "Regularized Geometry of the Loop Space" (2015). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2320.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2320