The semiclassical approximation for the Chern–Simons partition function

1997/09/30 by David H. Adams, David Adams
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Chern–Simons theory #Combinatorics #Function (biology) #Gauge theory #Invariant (physics) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Partition (number theory) #Partition function (quantum field theory) #Physics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scale invariance #Semiclassical physics #dg-ga #hep-th #math.DG #math.QA #q-alg

paper · pdf · doi:10.1016/s0370-2693(97)01343-9

published as Phys.Lett. B417 (1998) 53-60 · 14 p., latex (a typo corrected), to appear in Phys.Lett.B

arxiv created 1997/10/25 · openalex publication_date 1998/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The semiclassical approximation for the partition function in Chern-Simons gauge theory is derived using the invariant integration method. Volume and scale factors which were undetermined and had to be fixed by hand in previous derivations are automatically taken account of in this framework. Agreement with Witten's exact expressions for the partition function in the weak coupling (large k) limit is verified for gauge group SU(2) and spacetimes S³, S² x S¹, S¹ x S¹ x S¹ and L(p,q).

Citations

• A largek asymptotics of Witten's invariant of Seifert manifolds
• Quantum field theory and the Jones polynomial
• Phase and scaling properties of determinants arising in topological field theories
• R-Torsion and the Laplacian on Riemannian manifolds
• Invariants of 3-manifolds via link polynomials and quantum groups
• Spectral asymmetry and Riemannian geometry. II