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arXiv · 2107.06987

A Poisson Algebra on the Hida Test Functions and a Quantization using the Cuntz Algebra

Wolfgang Bock·Vyacheslav Futorny·Mikhail Neklyudov
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Abstract

In this note we define one more way of quantization of classical systems. The quantization we consider is an analogue of classical Jordan-Schwinger (J.-S.) map which has been known and used for a long time by physicists. The difference, comparing to J.-S. map, is that we use generators of Cuntz algebra $\mathcal{O}_{\infty}$ (i.e. countable family of mutually orthogonal partial isometries of separable Hilbert space) as a "building blocks" instead of creation-annihilation operators. The resulting scheme satisfies properties similar to Van Hove prequantization i.e. exact conservation of Lie bracket and linearity.

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Wolfgang Bock, Vyacheslav Futorny, Mikhail Neklyudov. 2021-07-14. A Poisson Algebra on the Hida Test Functions and a Quantization using the Cuntz Algebra. https://doi.org/10.1007/s11005-022-01507-4

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