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The classical matter fields are sections of a vector bundle E with base manifold M, and the space L2(E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of $${C_b^\infty(M)}$$ on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum context, we show that this module action...
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