Abstract
The aim of this work is to study the Berezin quantization of a Gaussian state. The result is another Gaussian state that depends on a quantum parameter $\alpha$, that describes the relationship between the classical and quantum vision. The compression parameter $\lambda >0$ is associated to the harmonic oscillator semigroup.
Highlights
Open AccessThis paper is devoted to the study of the quantization of Gaussian states
The aim of this work is to study the Berezin quantization of a Gaussian state. The result is another Gaussian state that depends on a quantum parameter α, which describes the relationship between the classical and quantum vision
The choice of the Berezin quantization is due to the fact that we will consider Gaussian functions on n instead 2n and, for this reason, a good scheme of quantization of n is the Berezin quantization
Summary
This paper is devoted to the study of the quantization of Gaussian states. Let us consider a function f ( x, p) , with ( x, p) ∈ 2n , denoted by Bα ( f ) as its Berezin quantization. It is well known that this scheme of quantization in comparison with the Weyl quantization presents “a few problems”: for example, it doesn’t preserve polynomial relations, the product rules are more complicated than Weyl quantization and the equivalent of Eherenfest theorem doesn’t hold. This scheme of quantization is rarely used to describe the system dynamics. Is the inner product of elements of L2 ( ) In this theorem the quantum parameter has been fixed to 1 as it is convention with the natural units
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