Trace extensions, determinant bundles, and gauge group cocycles
  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. 
Joakim Arnlind and Jouko Mickelsson