Moyal quantization of 2+1-dimensional Galilean systems

DOI10.1063/1.529939zbMath0788.22025OpenAlexW2044480196MaRDI QIDQ4030942

Ángel Ballesteros, Manuel Gadella, Mariano A. del Olmo

Publication date: 1 April 1993

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529939

zbMATH Keywords

coadjoint orbitsunitary irreducible representationsGalilean groupStratonovich-Weyl kernels

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Geometric quantization (53D50) Applications of linear algebraic groups to the sciences (20G45)

Related Items

Transitive symplectic manifolds in 1+2 dimensions, The projective unitary irreducible representations of the Galilei group in 1+2 dimensions, (2 + 1)D exotic Newton-Hooke symmetry, duality and projective phase, DYNAMICS IN NON-COMMUTATIVE SPACES AND GENERALIZATIONS, Electric Chern--Simons term, enlarged exotic Galilei symmetry and noncommutative plane, EXOTIC GALILEAN SYMMETRY AND THE HALL EFFECT, Planar Carrollean dynamics, and the Carroll quantum equation, Quantum mechanics as a matrix symplectic geometry, Moyal quantization on the cylinder, Dynamics of a noncommutative monopole, Enlarged NH symmetries: particle dynamics and gauge symmetries, Quantization on a two-dimensional phase space with a constant curvature tensor., Ray representations of N(≤2)+1-dimensional Galilean group, Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry, \((2+1)\) Newton-Hooke classical and quantum systems, (1 + 1) Newton–Hooke group for the simple and damped harmonic oscillator, States in the Hilbert space formulation and in the phase space formulation of quantum mechanics, The noncommutative Landau problem, Galilean exotic planar supersymmetries and nonrelativistic supersymmetric wave equations, Acceleration-extended Galilean symmetries with central charges and their dynamical realizations, Galilean-invariant \((2+1)\)-dimensional models with a Chern-Simons-like term and \(D=2\) noncommutative geometry, Geometrical origin of the \(\ast\)-product in the Fedosov formalism, \((2+1)\)-dimensional models with a Chern-Simons-like term and noncommutative geometry

Cites Work

• Parity operator and quantization of \(\delta\)-functions
• Local representation groups
• Relativistic quantum kinematics in the Moyal representation
• Locally operating realizations of transformation Lie groups
• The Stratonovich–Weyl correspondence for one-dimensional kinematical groups
• On local and global equivalence of wave functions
• On the Quantum Correction For Thermodynamic Equilibrium
• Moyal quantization with compact symmetry groups and noncommutative harmonic analysis
• Galilei Group and Nonrelativistic Quantum Mechanics
• On the Contraction of Groups and Their Representations