Topological interpretations of lattice gauge field theory

Doug Bullock, Charles Frohman, Joanna Kania-Bartoszyńska

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We construct lattice gauge field theory based on a quantum group on a lattice of dimension one. Innovations include a coalgebra structure on the connections and an investigation of connections that are not distinguishable by observables. We prove that when the quantum group is a deformation of a connected algebraic group G (over the complex numbers), then the algebra of observables forms a deformation quantization of the ring of G-characters of the fundamental group of the lattice. Finally, we investigate lattice gauge field theory based on quantum SL2ℂ, and conclude that the algebra of observables is the Kauffman bracket skein module of a cylinder over a surface associated to the lattice.

Original languageEnglish
Pages (from-to)47-81
Number of pages35
JournalCommunications in Mathematical Physics
Volume198
Issue number1
DOIs
StatePublished - 1998

Fingerprint

Dive into the research topics of 'Topological interpretations of lattice gauge field theory'. Together they form a unique fingerprint.

Cite this