Symplectic quantum mechanics

DOI10.1016/j.aop.2004.03.009zbMath1053.81061OpenAlexW1971398751MaRDI QIDQ1877784

Yanyan Li

Publication date: 19 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.aop.2004.03.009

zbMATH Keywords

phase spaceGalilei groupWeyl productWagner function

Mathematics Subject Classification ID

Coherent states (81R30) Geometry and quantization, symplectic methods (81S10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Covariant wave equations in quantum theory, relativistic quantum mechanics (81R20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (18)

Quark-antiquark effective potential in symplectic quantum mechanics ⋮ Stefan-Boltzmann law and Casimir effect for the scalar field in phase space at finite temperature ⋮ Phase space Schrödinger equation and quadratic friction ⋮ Symplectic field theories: scalar and spinor representations ⋮ Non-commutative geometry and symplectic field theory ⋮ Quantum mechanics on phase space and the Coulomb potential ⋮ Zeeman effect in phase space ⋮ On scalar electromagnetism in phase space ⋮ Fractional effective quark-antiquark interaction in symplectic quantum mechanics ⋮ Spin-1/2 particles in phase space: Casimir effect and Stefan-Boltzmann law at finite temperature ⋮ Quantum field theory in phase space ⋮ Supersymmetric symplectic quantum mechanics ⋮ Quantum mechanics on phase space: The hydrogen atom and its Wigner functions ⋮ Quantum field theory on toroidal topology: algebraic structure and applications ⋮ SOLUTIONS FOR THE LANDAU PROBLEM USING SYMPLECTIC REPRESENTATIONS OF THE GALILEI GROUP ⋮ Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory ⋮ Analytical solution for the Gross-Pitaevskii equation in phase space and Wigner function ⋮ Projective representation of the Galilei group for classical and quantum–classical systems*

Cites Work

• Unnamed Item
• The Cangemi-Jackiw manifold in high dimensions and symplectic structure
• Foundations of phase-space quantum mechanics
• Wigner functions in covariant and single-time formulations
• Discrete coherent states and probability distributions in finite-dimensional spaces
• \(W^*\)-algebra, Poincaré group, and quantum kinetic theory
• The Moyal-Lie theory of phase space quantum mechanics
• Relativistic quantum kinematics in the Moyal representation
• Space-time geometry of relativistic particles in four-dimensional phase space
• Galilean Duffin Kemmer Petiau algebra and symplectic structure
• On the Quantum Correction For Thermodynamic Equilibrium
• Gauge-invariant formulations of lineal gravities

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