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- W4297835766 abstract "Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group $SU_q(2)$ is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples of this new Toeplitz quantization. Annihilation and creation operators are defined as densely defined Toeplitz operators acting in a quantum Hilbert space, and their commutation relations are discussed. At this point Planck's constant is introduced into the theory. Due to the possibility of non-commuting symbols, there are now two definitions for anti-Wick quantization; these two definitions are equivalent in the commutative case. The Toeplitz quantization introduced here satisfies one of these definitions, but not necessarily the other. This theory should be considered as a second quantization, since it quantizes non-commutative (that is, already quantum) objects. The quantization theory presented here has two essential features of a physically useful quantization: Planck's constant and a Hilbert space where natural, densely defined operators act." @default.
- W4297835766 created "2022-10-01" @default.
- W4297835766 creator A5022767810 @default.
- W4297835766 date "2013-08-25" @default.
- W4297835766 modified "2023-09-30" @default.
- W4297835766 title "Toeplitz Quantization for Non-commutating Symbol Spaces such as $SU_q(2)$" @default.
- W4297835766 doi "https://doi.org/10.48550/arxiv.1308.5454" @default.
- W4297835766 hasPublicationYear "2013" @default.
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