Gravitational anomalies, gerbes, and hamiltonian quantization

TL;DR

This paper extends the mathematical framework for analyzing anomalies in quantum field theory by incorporating gravitational effects into the existing gerbe-based approach for Hamiltonian quantization of chiral fermions.

Contribution

It generalizes previous methods to include gravitational Schwinger terms using gerbes and the family index theorem, advancing the understanding of gravitational anomalies in quantum systems.

Findings

Derived gravitational Schwinger terms in Hamiltonian quantization.

Extended gerbe-based methods to include gravitational effects.

Connected anomalies with topological and geometric structures.

Abstract

In [Carey, A.L., J. Mickelsson, and M. K. Murray: Comm. Math. Phys. 183, 707 (1997)] Schwinger terms in hamiltonian quantization of chiral fermions coupled to vector potentials were computed, using some ideas from the theory of gerbes, with the help of the family index theorem for a manifold with boundary. Here, we generalize this method to include gravitational Schwinger terms.