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arXiv · hep-th/0306025

A "general boundary" formulation for quantum mechanics and quantum gravity

Robert Oeckl
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Abstract

I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such ``general boundary'' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a ``general boundary'' formulation. Surprisingly, even in the non-relativistic case, features normally associated with quantum field theory emerge from consistency conditions. This includes states with arbitrary particle number and pair creation. I also note how three dimensional quantum gravity is an example for a realization of both proposals and suggest to apply them to four dimensional quantum gravity.

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Robert Oeckl. 2003-10-16. A "general boundary" formulation for quantum mechanics and quantum gravity. https://doi.org/10.1016/j.physletb.2003.08.043

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