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

2019/05/25 by Merav Hadad, Hadad, Merav, Levy Rosenblum +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.48550/arxiv.1905.10665

openalex publication_date 2019/05/25 · arxiv created 2019/11/12 · arxiv updated 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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