English

Trace extensions, determinant bundles, and gauge group cocycles

High Energy Physics - Theory 2007-05-23 v2 Differential Geometry

Abstract

We study the geometry of determinant line bundles associated to Dirac operators on compact odd dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions and associated multiplicative renormalized determinants.

Keywords

Cite

@article{arxiv.hep-th/0205126,
  title  = {Trace extensions, determinant bundles, and gauge group cocycles},
  author = {Joakim Arnlind and Jouko Mickelsson},
  journal= {arXiv preprint arXiv:hep-th/0205126},
  year   = {2007}
}

Comments

clarifications and improvements in the text, added references; results unchanged

R2 v1 2026-07-22T15:10:48.681Z