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

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