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

Merav Hadad; Levy Rosenblum

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arXiv · 1905.10665

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

Merav Hadad·Levy Rosenblum

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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.

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Merav Hadad, Levy Rosenblum. 2019-05-25. Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories. https://arxiv.org/abs/1905.10665

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