{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Regularized Geometry of the Loop Space","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/76397"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"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."},{"label":"dcterms.available","value":"2017-09-20T16:50:10Z"},{"label":"dcterms.contributor","value":"Movshev, Mikhail"},{"label":"dcterms.creator","value":"Hao, Cheng"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:50:10Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:50:10Z"},{"label":"dcterms.description","value":"Department of Mathematics."},{"label":"dcterms.extent","value":"55 pg."},{"label":"dcterms.format","value":"Monograph"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/76397"},{"label":"dcterms.issued","value":"2015-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:50:10Z (GMT). No. of bitstreams: 1\nHao_grad.sunysb_0771E_12550.pdf: 384829 bytes, checksum: 17f521d76349eec11ad02f1e0d764d23 (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"loop space, mass gap, regularized geometry, sigma model"},{"label":"dcterms.title","value":"Regularized Geometry of the Loop Space"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/11%2F37%2F15%2F113715486253978618237631235647088645057/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/11%2F37%2F15%2F113715486253978618237631235647088645057","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}