Solution of the noncanonicity puzzle in General Relativity: a new Hamiltonian formulation
F. Cianfrani, M. Lulli, G. Montani
备注：
Accepted for Publication in Physics Letters B. Major revisions in Canonical Quantization section for operator ordering choice and in the definition of 'gauged canonicity' for the classical analysis. 19 pages single column
We study the transformation leading from Arnowitt, Deser, Misner (ADM) Hamiltonian formulation of General Relativity (GR) to the $ΓΓ$ metric Hamiltonian formulation derived from the Lagrangian density which was firstly proposed by Einstein. We classify this transformation as gauged canonical - i.e. canonical modulo a gauge transformation. In such a study we introduce a new Hamiltonian formulation written in ADM variables which differs from the usual ADM formulation mainly in a boundary term firstly proposed by Dirac. Performing the canonical quantization procedure we introduce a new functional phase which contains an explicit dependence on the fields characterizing the 3+1 splitting. Given a specific regularization procedure our new formulation privileges the symmetric operator ordering in order to: have a consistent quantization procedure, avoid anomalies in constraints algebra, be equivalent to the Wheeler-DeWitt (WDW) quantization. Furthermore we show that this result is consistent with a path-integral approach.
Is time travel possible? What is Einstein's theory of relativity mathematically predicting in that regard? Is time travel related to the so-called clock 'paradoxes' of relativity and if so how? Is there any accurate experimental evidence of the phenomena regarding the different flow of time predicted by General Relativity and is there any possible application of the temporal phenomena predicted by relativity to our everyday life? Which temporal phenomena are predicted in the vicinities of a rotating body and of a mass-energy current, and do we have any experimental test of the occurrence of th…
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