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
compression parameter λ>0 is associated to the
harmonic oscillator semigroup.
References
[1]
Berezin, F.A. (1975) General Concept of Quantization. Communications in Mathematical Physics, 40, 153-174. https://doi.org/10.1007/BF01609397
[2]
Englis, M. (2016) An Excursion into Berezin-Toeplitz Quantization and Related Topics. In: Bahns, D., Bauer, W. and Witt, I., Eds., Quantization, PDEs, and Geometry. Operator Theory: Advances and Applications, 251, 69-115. https://doi.org/10.1007/978-3-319-22407-7_2
[3]
Englis, M. (2006) Berezin and Berezin-Toeplitz Quantizations for General Function Spaces. Revista Matemática Complutense, 19, 385-430.
[4]
Ali, S.T. and Englis, M. (2005) Quantization Methods: A Guide for Physicists and Amalysts. Reviews in Mathematical Physics, 17, 391-490. https://doi.org/10.1142/S0129055X05002376
[5]
Berezin, F.A. and Shubin, M.A. (1970) Symbols of Operators and Quantization. Proceedings of the Colloquia Math. Soc. Janos Bolyai, Tihany, 1970, 21-52.
[6]
Griffiths, D.J. (2004) Introduction to Quantum Mechanics. 2nd Edition, Pearson.
[7]
Hall, B.C. (2013) Quantum Theory for Mathematicians. Springer, Graduate Texts in Mathematics.
[8]
Stroethoff, K. (1997) The Berezin Transform and Operators on Spaces of Analytic Functions. Linear Operators Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, Warszawa, Vol. 38.
[9]
Zhu, K. (2015) Uncertainty Principles for the Fock Space. Preprint.
[10]
Weyl, H. (1950) Gruppentheorie und Quantenmechanik. S. Hirzel, Leipzig, 1928. Revised English Edition: “The Theory of Groups and Quantum Mechanics”, Methuen, London, 1931, Reprinted by Dover, New York, 1950.
