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

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

2003-06-03

arxiv.org/abs/hep-th/0306025v2

Phys.Lett. B575 (2003) 318-324

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, 2 figures, LaTeX + revtex4 + eps; abstract shortened, other minor corrections, references updated

Scientific paper

10.1016/j.physletb.2003.08.043

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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