dorsal/arxiv
View SchemaWigner-Weyl-Moyal Formalism on Algebraic Structures
| Authors | Frank Antonsen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9608042 |
| URL | https://arxiv.org/abs/quant-ph/9608042 |
| Journal | Int.J.Theor.Phys. 37 (1998) 697-758 |
Abstract
We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a deformation of the classical phase-space: instead of being a vector space it becomes a manifold, the topology of which is given by the commutator relations. It is shown in fact that the classical phase-space, for a semi-simple Lie algebra, becomes a homogenous symplectic manifold. The symplectic product is also deformed. We finally make some comments on how to generalize to $C^*$-algebras and other operator algebras too.
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"abstract": "We first introduce the Wigner-Weyl-Moyal formalism for a theory whose\nphase-space is an arbitrary Lie algebra. We also generalize to quantum Lie\nalgebras and to supersymmetric theories. It turns out that the\nnon-commutativity leads to a deformation of the classical phase-space: instead\nof being a vector space it becomes a manifold, the topology of which is given\nby the commutator relations. It is shown in fact that the classical\nphase-space, for a semi-simple Lie algebra, becomes a homogenous symplectic\nmanifold. The symplectic product is also deformed. We finally make some\ncomments on how to generalize to $C^*$-algebras and other operator algebras\ntoo.",
"arxiv_id": "quant-ph/9608042",
"authors": [
"Frank Antonsen"
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],
"journal_ref": "Int.J.Theor.Phys. 37 (1998) 697-758",
"title": "Wigner-Weyl-Moyal Formalism on Algebraic Structures",
"url": "https://arxiv.org/abs/quant-ph/9608042"
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