Many-Body Wigner Quantum Systems

Abstract

We present examples of many-body Wigner quantum systems. The position and the momentum operators ${\mathbf{R}}_A$ and ${\mathbf{P}}_A,A=1,\dots ,n+1$, of the particles are noncanonical and are chosen so that the Heisenberg and the Hamiltonian equations are identical. The spectrum of the energy with respect to the centre of mass is equidistant and has finite number of energy levels. The composite system is spread in a small volume around the centre of mass and within it the geometry is noncommutative. The underlying statistics is an exclusion statistics.

20 pages, PlainTex

References in corpus (4)

• Para-Statistics as Lie-super Triple Systems
• Wigner quantum oscillators. Osp(3/2) oscillators
• Many-body States and Operator Algebra for Exclusion Statistics
• Wigner Quantum Oscillators

Cited by in corpus (27)

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• The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
• Jacobson generators, Fock representations and statistics of sl(n+1)
• A non-commutative n-particle 3D Wigner quantum oscillator
• Harmonic oscillator chains as Wigner Quantum Systems: periodic and fixed wall boundary conditions in gl(1|n) solutions
• Harmonic oscillators coupled by springs: discrete solutions as a Wigner Quantum System
• On the algebra of symmetries of Laplace and Dirac operators
• Microscopic and macroscopic properties of A-superstatistics
• Representations of the Lie Superalgebra gl(1|n) in a Gel'fand-Zetlin Basis and Wigner Quantum Oscillators
• A q-deformation of the parastatistics and an alternative to the Chevalley description of $U_q[osp(2n+1/2m)]$
• Exclusion statistics,operator algebras and Fock space representations
• A classification of generalized quantum statistics associated with the exceptional Lie (super)algebras
• Analytically solvable Hamiltonians for quantum systems with a nearest neighbour interaction
• Highest weight irreducible representations of the quantum algebra $U_h(A_{\infty })$
• Solutions of the compatibility conditions for a Wigner quantum oscillator
• A description of the quantum superalgebra $U_q[sl(n+1|m)]$ via creation and annihilation generators
• A classification of generalized quantum statistics associated with basic classical Lie superalgebras
• Interpretation and Extension of the Green's Ansatz for Paraparticles
• Wigner quantization of some one-dimensional Hamiltonians
• Quantum Mechanics with Difference Operators
• Wigner quantum systems (Lie superalgebraic approach)
• Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matrix
• Representations of the orthosymplectic Lie superalgebra osp(1|4) and paraboson coherent states
• Chiral bosons on Bargmann space associated with A${}_r$ Statistics
• Highest weight irreducible representations of the Lie superalgebra $gl(1/\infty )$
• Jacobson generators of the quantum superalgebra $U_q[sl(n+1|m)]$ and Fock representations
• Irreducible highest weight representations of the quantum algebra $U_h(A_{\infty })$