Obstacles to the quantization of general relativity using symplectic structures
Abstract
In this paper I give overviews of the polysymplectic approach to covariant Hamiltonian field theory and the simplest geometric quantization of classical particle theories. I then give a synopsis of a recently proposed toy model for applying this geometric quantization map to polysymplectic field theory. I show that no special difficulties arise when this toy model is applied to general relativity. I then sketch the reasons why the standard tools of covariant Hamiltonian field theory are not up to the challenge of GR, so that the resulting quantum theory cannot be taken seriously. A few remarks are given about prospects for future work.
Cite
@article{arxiv.2012.06877,
title = {Obstacles to the quantization of general relativity using symplectic structures},
author = {Tom McClain},
journal= {arXiv preprint arXiv:2012.06877},
year = {2020}
}
Comments
10 pages. Based on a presentation at the Second Hermann Minkowski Meeting on the Foundations of Spacetime Physics. Appears in "Spacetime: 1909 - 2019." Reinoud Jan Slagter and Zoltan Keresztes (Editors). Minkowski Institute Press, 2020