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Quantization by Quadratic Polynomials in Creation and Annihilation Operators

In: Quantization, Coherent States, and Complex Structures

Author

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  • Wojtek Słowikowski

    (Aarhus University, Institute of Mathematics)

Abstract

Let us fix a number q = 1 or −1. To a given Hubert space H, , we attach an algebra Γ0 H generated by H and a unity φ called the vacuum. We call Γ0 H a Fock algebra if the scalar product from H is extended over Γ0 H in such a way that = 1 and, for every x ∈ H, the operator a +(x) of multiplication by x admits the adjoint a(x), defined on the whole Γ0 H and annihilating the vacuum, i.e. = for all f, g ∈ Γ0 H and a(x)φ = 0. We assume that a(x) fulfills the q-Leibnitz rule, i.e. [a(x), a +(y)] q = I, where [A, B] q = AB − qBA.

Suggested Citation

  • Wojtek Słowikowski, 1995. "Quantization by Quadratic Polynomials in Creation and Annihilation Operators," Springer Books, in: J.-P. Antoine & S. Twareque Ali & W. Lisiecki & I. M. Mladenov & A. Odzijewicz (ed.), Quantization, Coherent States, and Complex Structures, pages 233-234, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1060-8_25
    DOI: 10.1007/978-1-4899-1060-8_25
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