A Doubled Discretization of Abelian Chern-Simons Theory

1997/04/21 by David H. Adams, David Adams · 30 citations
Mathematics · Physics and Astronomy · #Abelian group #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Chern–Simons theory #Connection (principal bundle) #Discretization #Fermion #Gauge theory #Geometry #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Spinor #Spinor field #Theoretical physics #dg-ga #hep-lat #hep-th #math.DG #math.QA #q-alg

paper · pdf · doi:10.1103/physrevlett.78.4155

published in Physical Review Letters 78(22), 4155-4158 (American Physical Society) · 5 pages, revtex, 2 ps figures (epsf required). To appear in Phys.Rev.Lett

arxiv created 1997/04/21 · openalex publication_date 1997/06/02 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A new discretization of a doubled, i.e., BF, version of the pure Abelian Chern-Simons theory is presented. It reproduces the continuum expressions for the topological quantities of interest in the theory, namely, the partition function and correlation function of Wilson loops. Similarities with free spinor field theory are discussed, which are of interest in connection with lattice fermion doubling.

Citations

• Quantum field theory and the Jones polynomial
• Analytic torsion and R-torsion of Riemannian manifolds
• Quarks, Gluons and Lattices
• Phase and scaling properties of determinants arising in topological field theories
• Analytic Torsion and The Heat Equation
• R-Torsion and the Laplacian on Riemannian manifolds
• Three-Dimensional Massive Gauge Theories