dorsal/arxiv
View SchemaPoisson-Lie Structures and Quantisation with Constraints
| Authors | Petre Diţă |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9809083 |
| URL | https://arxiv.org/abs/quant-ph/9809083 |
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 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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"abstract": "We develop here a simple quantisation formalism that make use of Lie algebra\nproperties of the Poisson bracket. When the brackets $\\{H,\\phi_i\\}$ and\n$\\{\\phi_i,\\phi_j\\}$, where $H$ is the Hamiltonian and $\\phi_i$ are primary and\nsecondary constraints, can be expressed as functions of $H$ and $\\phi_i$\nthemselves, the Poisson bracket defines a Poisson-Lie structure. When this\nalgebra has a finite dimension a system of first order partial differential\nequations is established whose solutions are the observables of the theory. The\nmethod is illustrated with a few examples.",
"arxiv_id": "quant-ph/9809083",
"authors": [
"Petre Di\u0163\u0103"
],
"categories": [
"quant-ph"
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"title": "Poisson-Lie Structures and Quantisation with Constraints",
"url": "https://arxiv.org/abs/quant-ph/9809083"
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