Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories

Merav Hadad; Levy Rosenblum

doi:10.1016/j.physletb.2019.135144

Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories

Merav Hadad, Levy Rosenblum

Physics discipline

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Abstract

Recently it was found that quantum gravity theories may involve constructing a quantum theory on non-Cauchy hypersurfaces. However this is problematic since the ordinary Poisson brackets are not causal in this case. We suggest a method to identify classical brackets that are causal on 2+1 non-Cauchy hypersurfaces and use it in order to show that the evolution of scalars and vectors fields in the 3rd spatial direction can be constructed by using a Hamilton-like procedure. Finally, we discuss the relevance of this result to quantum gravity.

Original language	English
Article number	135144
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	801
DOIs	https://doi.org/10.1016/j.physletb.2019.135144
State	Published - 10 Feb 2020

Bibliographical note

Funding Information:
We thank Oded Kenneth for reading the first manuscript of the paper and for his fruitful comments. This research was supported by The Open University of Israel's Research Fund (grant no. 509565 ).

Publisher Copyright:
© 2019 The Authors

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Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories

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