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AIP conference proceedings

Q-deformation of bosonic paraquantum trilinear commutation relations

M. H. Traikia, N. Mebarki

Published Jan 1, 2012• 0 citations
Publisher

Abstract

Using a weak deformation of the Weyl-Heisenberg algebra of a paraquantization of order 2. After defining a generalized commutation and anti-commutation relations, modified triliniar commutation relations are derived.
DOI
10.1063/1.4715452

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We discuss the q deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the q-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. The von Neumann theorem in Quantum Mechanics (QM) states that for systems with finite number of degrees of freedom the representations of the canonical commutation relations (ccr), also called the Weyl representations, are each other unitarily equivalent. In the limit of infinite number of degrees of freedom, namely in Quantum Field Theory
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