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Deformation quantization on a Hilbert space

Giuseppe Dito
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Abstract

We study deformation quantization on an infinite-dimensional Hilbert space $W$ endowed with its canonical Poisson structure. The standard example of the Moyal star-product is made explicit and it is shown that it is well defined on a subalgebra of $C^\infty(W)$. A classification of inequivalent deformation quantizations of exponential type, containing the Moyal and normal star-products, is also given.

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Giuseppe Dito. 2004-06-28. Deformation quantization on a Hilbert space. https://arxiv.org/abs/math/0406583

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