On the ADM decomposition of the 5-D Kaluza-Klein model

Details On the ADM decomposition of the 5-D Kaluza-Klein model On the ADM decomposition of the 5-D Kaluza-Klein model

2006-01-24

arxiv.org/abs/gr-qc/0601101v1

Int.J.Mod.Phys. D15 (2006) 559-582

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, no figures, to appear on IJMPD

Scientific paper

10.1142/S0218271806008309

Our purpose is to recast KK model in terms of ADM variables. We examine and solve the problem of the consistency of this approach, with particular care about the role of the cylindricity hypothesis. We show in details how the KK reduction commutes with the ADM slicing procedure and how this leads to a well defined and unique ADM reformulation. This allows us to consider the hamiltonian formulation of the model and can be the first step for the Ashtekar reformulation of the KK scheme. Moreover we show how the time component of the gauge vector arises naturally from the geometrical constraints of the dynamics; this is a positive check for the autoconsistency of the KK theory and for an hamiltonian description of the dynamics which wants to take into account the compactification scenario: this result enforces the physical meaning of KK model.

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