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.
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - 10 Feb 2020|
Bibliographical noteFunding 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 ).
© 2019 The Authors