A 'General boundary' formulation for quantum mechanics and quantum gravity

By R. Oeckl. 2003

172 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/673694d887bb31a0d4c1599aec95d407a5c59b2f

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Reformulating and Reconstructing Quantum Theory (2011, methodology): “The multi-time approach of Aharonov, Popescu, Tollaksen, and Vaidman [2] and the general boundary approach of Oeckl [61] can be understood to be doing something similar but are restricted to the pure state case.”
Flipped spinfoam vertex and loop gravity (2007, methodology): “Finally, the dynamics is specified by computing an amplitude for a state in the boundary Hilbert space [37, 38].”
The continuum limit of loop quantum gravity - a framework for solving the theory (2014, background): “The framework[23] introduces a generalization of Cauchy boundaries to boundaries of arbitrary regions, which is useful in this context.”
Phase space descriptions for simplicial 4D geometries (2008, methodology): “In particular, we used so far a ‘generalized boundary’ [40], namely the 3-sphere, where even for classical and continuous general relativity the question of wellposed initial values is unclear.”
Why Gauge? (2013, methodology): “We can formalize the observations in the previous section by using the covariant form of the dynamics [27] based on the boundary formalism [31].”
Loop Quantum Gravity (2003, background): “The idea behind this formalism is to consider semiclassical coherent states on finite boundaries of 4d regions, and compare the amplitude of such states with the amplitude of the same state over which field excitations are added [5, 145].”
A new look at loop quantum gravity (2010, background): “In a general covariant quantum theory, the dynamics can be given by associating an amplitude with each boundary state [36, 37].”
Zakopane lectures on loop gravity (2011, background): “3) on a foam with boundaries, as a function of the boundary state [23].”