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General remarks on harmonic analysis on homogeneous spaces suitable for tensor as well as spinor fields is presented using fibre bundle techniques. Then several examples are worked out.
Abstract: In ref. [1], 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.
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