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

TL;DR

This paper introduces a 'general boundary' approach to quantum theories, unifying quantum mechanics and quantum field theory through a topological quantum field theory framework, with implications for quantum gravity.

Contribution

It formalizes quantum theories as generalized topological quantum field theories using a boundary-based approach, extending to quantum gravity.

Findings

Non-relativistic quantum mechanics can be reformulated in the 'general boundary' framework.

Features like arbitrary particle number and pair creation emerge naturally.

Three-dimensional quantum gravity exemplifies the proposed formalism.

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.