TY - JOUR
T1 - Derivation of Hamilton-like equations on a non-Cauchy hypersurface and their expected connection to quantum gravity theories
AU - Hadad, Merav
AU - Rosenblum, Levy
N1 - Publisher Copyright:
© 2019 The Authors
PY - 2020/2/10
Y1 - 2020/2/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85077084201&partnerID=8YFLogxK
U2 - 10.1016/j.physletb.2019.135144
DO - 10.1016/j.physletb.2019.135144
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AN - SCOPUS:85077084201
SN - 0370-2693
VL - 801
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
M1 - 135144
ER -