Quantization by Quadratic Polynomials in Creation and Annihilation Operators

Wojtek Słowikowski
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Wojtek Słowikowski: Aarhus University, Institute of Mathematics

A chapter in Quantization, Coherent States, and Complex Structures, 1995, pp 233-234 from Springer

Abstract: 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.

Date: 1995
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DOI: 10.1007/978-1-4899-1060-8_25

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