Can We Look at The Quantisation Rules as Constraints?

Details Can We Look at The Quantisation Rules as Constraints? Can We Look at The Quantisation Rules as Constraints?

1997-03-26

arxiv.org/abs/dg-ga/9703019v1

Nucl.Phys.Proc.Suppl. B57 (1997) 223

Physics

High Energy Physics

High Energy Physics - Theory

4-pages, latex

Scientific paper

10.1016/S0920-5632(97)00383-6

In this paper we explore the idea of looking at the Dirac quantisation conditions as $\hbar$-dependent constraints on the tangent bundle to phase-space. Starting from the path-integral version of classical mechanics and using the natural Poisson brackets structure present in the cotangent bundle to the tangent bundle of phase- space, we handle the above constraints using the standard theory of Dirac for constrained systems. The hope is to obtain, as total Hamiltonian, the Moyal operator of time-evolution and as Dirac brackets the Moyal ones. Unfortunately the program fails indicating that something is missing. We put forward at the end some ideas for future work which may overcome this failure.

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