Quantum mechanics on noncommutative plane and sphere from constrained systems

DOI10.1016/S0370-2693(02)01262-5zbMath0989.81050arXivhep-th/0201034OpenAlexW3105967627MaRDI QIDQ5960490

Alexei A. Deriglazov

Publication date: 7 April 2002

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0201034

zbMATH Keywords

magnetic monopoleMoyal productconstrained system canonical quantizationLagrangian actionssecond class constraintsspace variable dynamics

Mathematics Subject Classification ID

Noncommutative geometry in quantum theory (81R60) Constrained dynamics, Dirac's theory of constraints (70H45)

Related Items (18)

Phases in noncommutative quantum mechanics on (pseudo)sphere ⋮ LAGRANGIAN FORMULATION FOR NONCOMMUTATIVE NONLINEAR SYSTEMS ⋮ Noncommutative cosmological models coupled to a perfect fluid and a cosmological constant ⋮ The effect of singular potentials on the harmonic oscillator ⋮ Dynamics of a Dirac fermion in the presence of spin noncommutativity ⋮ Representations of non-commutative quantum mechanics and symmetries ⋮ Spin Hall effect in noncommutative coordinates ⋮ The transformation of commutative phase space to noncommutative one, and its Lorentz transformation-like forms ⋮ Variational problem for Hamiltonian system on so(k, m) Lie–Poisson manifold and dynamics of semiclassical spin ⋮ The aharonov-bohm effect in noncommutative quantum mechanics ⋮ EQUIVALENCE BETWEEN DIFFERENT CLASSICAL TREATMENTS OF THE O(N) NONLINEAR SIGMA MODEL AND THEIR FUNCTIONAL SCHRÖDINGER EQUATIONS ⋮ Canonical and Lie-algebraic twist deformations of Carroll, para-Galilei and Static Hopf algebras ⋮ NONCOMMUTATIVITY FROM THE SYMPLECTIC POINT OF VIEW ⋮ On uncertainty relations in noncommutative quantum mechanics ⋮ COMMUTATOR ANOMALY IN NONCOMMUTATIVE QUANTUM MECHANICS ⋮ Twist deformation of rotationally invariant quantum mechanics ⋮ Gauge invariant actions for the noncommutative phase-space relativistic particle ⋮ Noncommutative relativistic particle on the electromagnetic background

Cites Work

• Reducible systems and embedding procedures in the canonical formalism
• Galilean-invariant \((2+1)\)-dimensional models with a Chern-Simons-like term and \(D=2\) noncommutative geometry
• Constrained quantization of open string in background \(B\) field and noncommutative D-brane
• Fine structure of constraints in Hamiltonian formulation
• Dirac quantization of open strings and noncommutativity in branes.
• Quantum mechanics on a noncommutative brane in M(atrix) theory
• Quantum mechanics on the noncommutative plane and sphere
• Supplementation of reducible constraints and the Green-Schwarz superstring

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