O(3,3)-like symmetries of coupled harmonic oscillators

DOI10.1063/1.530940zbMath0853.70013arXivquant-ph/9704005OpenAlexW1963871584MaRDI QIDQ4873254

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Publication date: 16 April 1996

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

Full work available at URL: https://arxiv.org/abs/quant-ph/9704005

zbMATH Keywords

Lorentz groupfour-dimensional phase spacegroup of unitary transformations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (11)

Noether-symmetry analysis using alternative Lagrangian representations ⋮ Dirac matrices and Feynman's rest of the universe ⋮ Quantum dynamics for general time-dependent three coupled oscillators based on an exact decoupling ⋮ DEFORMATION QUANTIZATION FOR COUPLED HARMONIC OSCILLATORS ON A GENERAL NONCOMMUTATIVE SPACE ⋮ Comment on: ``Entanglement in three coupled oscillators ⋮ A new kind of representations on noncommutative phase space ⋮ Coupled harmonic oscillator systems: An elementary algebraic decoupling approach ⋮ TWO COUPLED HARMONIC OSCILLATORS ON NONCOMMUTATIVE PLANE ⋮ An alternative approach to exact wave functions for time-dependent coupled oscillator model of charged particle in variable magnetic field ⋮ Poincaré symmetry from Heisenberg's uncertainty relations ⋮ $Sp(4; \mathbb{R})$ squeezing for Bloch four-hyperboloid via the non-compact Hopf map

Cites Work

• Symmetries of two-mode squeezed states
• On the Quantum Correction For Thermodynamic Equilibrium
• The Dirac gamma matrices as ‘‘relics’’ of a hidden symmetry?: As fundamental representations of the algebra sp(4,R)
• A Remarkable Representation of the 3 + 2 de Sitter Group
• Some Special Examples in Renormalizable Field Theory

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