Poisson-Lie Structures and Quantisation with Constraints

Details Poisson-Lie Structures and Quantisation with Constraints Poisson-Lie Structures and Quantisation with Constraints

1998-09-28

arxiv.org/abs/quant-ph/9809083v1

Physics

Quantum Physics

13 pages, Latex

Scientific paper

We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets $\{H,\phi_i\}$ and $\{\phi_i,\phi_j\}$, where $H$ is the Hamiltonian and $\phi_i$ are primary and secondary constraints, can be expressed as functions of $H$ and $\phi_i$ themselves, the Poisson bracket defines a Poisson-Lie structure. When this algebra has a finite dimension a system of first order partial differential equations is established whose solutions are the observables of the theory. The method is illustrated with a few examples.

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