{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/140007"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/140007","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"The Fock-Schwartz spin representation space","abstract":"In this thesis, we define and study a family of Sobolev-like subspaces (the “FockSobolev spaces”) and the corresponding Schwartz-like space (the “Fock-Schwartz space”) arising from the infinite-dimensional spin representation constructed by Pressley and Segal. In particular, we study the infinitesimal actions of the group of orientation-preserving diffeomorphisms, Diff⁺(𝑆¹), and the loop group 𝒧Spin(2𝑛), as well as the action of an infinite-dimensional Clifford algebra on the Fock-Sobolev spaces and Fock-Schwartz space. All of this work is motivated by the goal of constructing the Dirac-Ramond operator on the loop space of a string manifold.","abstract_html":"In this thesis, we define and study a family of Sobolev-like subspaces (the “FockSobolev spaces”) and the corresponding Schwartz-like space (the “Fock-Schwartz space”) arising from the infinite-dimensional spin representation constructed by Pressley and Segal. In particular, we study the infinitesimal actions of the group of orientation-preserving diffeomorphisms, Diff⁺(𝑆¹), and the loop group 𝒧Spin(2𝑛), as well as the action of an infinite-dimensional Clifford algebra on the Fock-Sobolev spaces and Fock-Schwartz space. All of this work is motivated by the goal of constructing the Dirac-Ramond operator on the loop space of a string manifold.","abstract_has_math":false,"creators":["Valiveti, Kaavya G."],"institution":"Massachusetts Institute of Technology","degree_name":"Doctoral","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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In particular, we study the infinitesimal actions of the group of orientation-preserving diffeomorphisms, Diff⁺(𝑆¹), and the loop group 𝒧Spin(2𝑛), as well as the action of an infinite-dimensional Clifford algebra on the Fock-Sobolev spaces and Fock-Schwartz space. All of this work is motivated by the goal of constructing the Dirac-Ramond operator on the loop space of a string manifold."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["The Fock-Schwartz spin representation space"]}]}],"canonical_facts":{"dc:contributor.advisor":["Melrose, Richard B."],"dc:contributor.department":["Massachusetts Institute of Technology. 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