Star products, duality and double Lie algebras

2006/09/06 by Olga V. Man’ko, Olga V. Man'ko, Vladimir I. Man'ko +4 · 1 citation
Physics and Astronomy · #Atomic and Subatomic Physics Research #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1016/j.physleta.2006.08.057

published as Phys.Lett. A360 (2007) 522-532 · 22 pages, no figures

arxiv created 2006/09/06 · openalex publication_date 2006/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantization of classical systems using the star-product of symbols of observables is discussed. In the star-product scheme an analysis of dual structures is performed and a physical interpretation is proposed. At the Lie algebra level duality is shown to be connected to double Lie algebras. The analysis is specified to quantum tomography. The classical tomographic Poisson bracket is found.

Citations

• Generalized Phase-Space Distribution Functions
• Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase
• On the principles of elementary quantum mechanics
• Density Operators and Quasiprobability Distributions
• Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams
• Quantum mechanics as a statistical theory
• On the Quantum Correction For Thermodynamic Equilibrium

Cited by

• Star products: a group-theoretical point of view