Quantum manifolds with classical limit

Details Quantum manifolds with classical limit Quantum manifolds with classical limit

2008-09-18

arxiv.org/abs/0809.3111v1

Physics

Mathematical Physics

31 pages

Scientific paper

We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the manifold structure of spacetime. In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value. We speculate on the possible relevance of this geometry to quantum field theory and gravity.

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