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Deformation in Phase Space

Oscar Arratia·Miguel A. Martin·Mariano A. Olmo
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Abstract

We review several procedures of quantization formulated in the framework of (classical) phase space M. These quantization methods consider Quantum Mechanics as a "deformation" of Classical Mechanics by means of the "transformation" of the commutative algebra of smooth functions on M in a new non-commutative algebra. These ideas lead in a natural way to Quantum Groups as deformation (or quantization, in a broad sense) of Poisson-Lie groups, which is also analysed here.

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Oscar Arratia, Miguel A. Martin, Mariano A. Olmo. 1998-05-18. Deformation in Phase Space. https://arxiv.org/abs/math-ph/9805016

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