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arXiv · 1905.00913

Toeplitz Quantization of a Free $ * $-Algebra

Stephen Bruce Sontz
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Abstract

In this note we quantize the free $ * $-algebra generated by finitely many variables, which is a new example of the theory of Toeplitz quantization of $ * $-algebras as developed previously by the author. This is achieved by defining Toeplitz operators with symbols in that non-commutative free $ * $-algebra. These are densely defined operators acting in a Hilbert space. Then creation and annihilation operators are introduced as special cases of Toeplitz operators, and their properties are studied.

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Stephen Bruce Sontz. 2019-05-02. Toeplitz Quantization of a Free $ * $-Algebra. https://arxiv.org/abs/1905.00913

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