Quantum mechanics and nonabelian theta functions for the gauge group SU(2)

• Autorzy: Răzvan Gelca , Alejandro Uribe
• Języki publikacji: EN

Abstrakty

EN

We propose a direction of study of nonabelian theta functions by establishing an analogy between the Weyl quantization of a one-dimensional particle and the metaplectic representation on the one hand, and the quantization of the moduli space of flat connections on a surface and the representation of the mapping class group on the space of nonabelian theta functions on the other. We exemplify this with the cases of classical theta functions and of the nonabelian theta functions for the gauge group SU(2). The emphasis of the paper is on this analogy and on the possibility of generalizing this approach to other gauge groups, and not on the results, of which some have appeared elsewhere.

Kategorie tematyczne

• 57M25: Knots and links in S 3
• 57R56: Topological quantum field theories
• 81T45: Topological field theories
• 81S10: Geometry and quantization, symplectic methods
• 81R50: Quantum groups and related algebraic methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 228
• Numer: 2
• Strony: 97-137

Daty

wydano

2015

Twórcy

autor

Răzvan Gelca

• Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, U.S.A.

autor

Alejandro Uribe

• Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.

Identyfikatory

DOI

10.4064/fm228-2-1