Abstract
We study the geometry of determinant line bundles associated with 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 nonmultiplicative renormalized determinants.
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Arnlind, J., Mickelsson, J. Trace Extensions, Determinant Bundles, and Gauge Group Cocycles. Letters in Mathematical Physics 62, 101–110 (2002). https://doi.org/10.1023/A:1021631405781
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DOI: https://doi.org/10.1023/A:1021631405781