Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matrix - Quantum PhysicsReport as inadecuate




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Abstract: In a system of coupled harmonic oscillators, the interaction can berepresented by a real, symmetric and positive definite interaction matrix. Thequantization of a Hamiltonian describing such a system has been done in thecanonical case. In this paper, we take a more general approach and look at thesystem as a Wigner quantum system. Hereby, one does not assume the canonicalcommutation relations, but instead one just requires the compatibility betweenthe Hamilton and Heisenberg equations. Solutions of this problem are related tothe Lie superalgebras gl1|n and osp1|2n. We determine the spectrum of theconsidered Hamiltonian in specific representations of these Lie superalgebrasand discuss the results in detail. We also make the connection with thewell-known canonical case.



Author: Gilles Regniers, Joris Van der Jeugt

Source: https://arxiv.org/







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