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Dirac operators coupled to vector potentials. (English) Zbl 0547.58033
The index for the Dirac operator on a manifold M with coefficients in a vector bundle E is considered in this paper as a virtual bundle on the space of connections on E modulo gauge equivalence. Its characteristic classes are described in terms of the curvature of the universal bundle on the product of M with the moduli space, and secondary characteristic classes on the space of connections itself are constructed. These relate to anomalies in the path integral formulation of quantum chromodynamics and an interpretation of the results involving determinants and the zeta function regularization is given.
Reviewer: N.Hitchin

MSC:
58J10 Differential complexes
34G20 Nonlinear differential equations in abstract spaces
81T08 Constructive quantum field theory
57R20 Characteristic classes and numbers in differential topology
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