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

Rəzvan Gelca, Alejandro Uribe

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)97-137
Number of pages41
JournalFundamenta Mathematicae
Volume228
Issue number2
DOIs
StatePublished - 2015

Keywords

  • Nonabelian theta functions
  • Reshetikhin-Turaev theory
  • Skein modules
  • Weyl quantization

Fingerprint Dive into the research topics of 'Quantum mechanics and nonabelian theta functions for the gauge group SU(2)'. Together they form a unique fingerprint.

Cite this