GEODESIC FLOWS, VON NEUMANN EQUATION AND QUANTUM MECHANICS ON NONCOMMUTATIVE CYLINDER

DOI10.1142/S0217732306020305zbMath1118.81046MaRDI QIDQ3430438

Partha Guha

Publication date: 22 March 2007

Published in: Modern Physics Letters A (Search for Journal in Brave)

zbMATH Keywords

von Neumann equationarea-preserving diffeomorphismMoyal deformed geodesic flows

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum field theory on curved space or space-time backgrounds (81T20) Geometry and quantization, symplectic methods (81S10) Deformation quantization, star products (53D55) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Cites Work

• A geometry for multidimensional integrable systems
• Discrete versions of some classical integrable systems and factorization of matrix polynomials
• Dressing operator approach to Moyal algebraic deformation of selfdual gravity
• Nonabelian KP hierarchy with Moyal algebraic coefficients
• Discretization and Moyal brackets
• Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top
• Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products
• The quantum structure of spacetime of the Planck scale and quantum fields
• A Lax pair for the two dimensional Euler equation
• Difference Operator Approach to the Moyal Quantization
• Quantum mechanics on the noncommutative plane and sphere
• Quantum mechanics on the noncommutative torus

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