| dc.identifier.uri | http://hdl.handle.net/11401/76397 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.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. | |
| dcterms.available | 2017-09-20T16:50:10Z | |
| dcterms.contributor | Khuri, Marcus | en_US |
| dcterms.contributor | Movshev, Mikhail | en_US |
| dcterms.contributor | Viro, Oleg | en_US |
| dcterms.contributor | Abanov, Alexander. | en_US |
| dcterms.creator | Hao, Cheng | |
| dcterms.dateAccepted | 2017-09-20T16:50:10Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:10Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 55 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76397 | |
| dcterms.issued | 2015-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:10Z (GMT). No. of bitstreams: 1
Hao_grad.sunysb_0771E_12550.pdf: 384829 bytes, checksum: 17f521d76349eec11ad02f1e0d764d23 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | loop space, mass gap, regularized geometry, sigma model | |
| dcterms.subject | Mathematics | |
| dcterms.title | Regularized Geometry of the Loop Space | |
| dcterms.type | Dissertation | |
