PoissonLie Structures and Quantisation with Constraints
Abstract
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 PoissonLie 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.
 Publication:

arXiv eprints
 Pub Date:
 September 1998
 DOI:
 10.48550/arXiv.quantph/9809083
 arXiv:
 arXiv:quantph/9809083
 Bibcode:
 1998quant.ph..9083D
 Keywords:

 Quantum Physics
 EPrint:
 13 pages, Latex