Wigner approach to quantization. Noncanonical quantization of two particles interacting via a harmonic potential

DOI10.1063/1.525230zbMath0502.70022OpenAlexW2133946102MaRDI QIDQ3968494

Tchavdar D. Palev

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1063/1.525230

zbMATH Keywords

harmonic potentialLie superalgebrasinternal degrees of freedomn-dimensionalthree-dimensional oscillatornon-canonicalclassical limiting caseWigner's approach to quantization

Mathematics Subject Classification ID

Hamilton's equations (70H05) General mathematical topics and methods in quantum theory (81Q99) Hamiltonian and Lagrangian mechanics (70H99) General models, approaches, and methods in mechanics of particles and systems (70G99)

Related Items (17)

Classification of generalized quantum statistics associated with the exceptional Lie (super)algebras ⋮ Compact quantum systems: Internal geometry of relativistic systems ⋮ Wigner quantum systems. Two particles interacting via a harmonic potential. I. Two-dimensional space ⋮ Jacobson generators, Fock representations and statistics of sl(n+1) ⋮ Transformations of some induced osp(3/2) modules in an so(3)⊕sp(2) basis ⋮ Parastatistics as Lie-supertriple systems ⋮ Bose description of the generalized Pauli spin operators and para super symmetry ⋮ Many-body Wigner quantum systems ⋮ Quantum mechanics with difference operators ⋮ Isotopic pairs and their representations ⋮ On the algebra of symmetries of Laplace and Dirac operators ⋮ The paraboson Fock space and unitary irreducible representations of the Lie superalgebra \({\mathfrak{osp}(1|2n)}\) ⋮ Highest weight irreducible representations of the Lie superalgebra gl(1|∞) ⋮ Angular momentum decomposition of the three-dimensional Wigner harmonic oscillator ⋮ Wigner oscillators, twisted Hopf algebras, and second quantization ⋮ Wigner quantization of some one-dimensional Hamiltonians ⋮ A classification of generalized quantum statistics associated with basic classical Lie superalgebras

Cites Work

• Fermi-Bose Similarity
• Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
• Fock space representations of the Lie superalgebra A(0,n)
• A Lie superalgebraic interpretation of the para-Bose statistics
• Phase-Space Formulation of the Dynamics of Canonical Variables
• Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations?
• A Note on the Quantum Rule of the Harmonic Oscillator
• A Generalized Method of Field Quantization

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