Quantum Groups and Von Neumann Theorem

Abstract

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.

9 pages, LaTeX. Paper published in 1994

Cited by in corpus (8)

• Fractals, coherent states and self-similarity induced noncommutative geometry
• Weyl-Gauge Symmetry of Graphene
• Thermo Field Dynamics and quantum algebras
• Bekenstein bound from the Pauli principle
• Quantization of Scalar Fields in Curved Background and Quantum Algebras
• Links. Relating different physical systems through the common QFT algebraic structure
• Thermal Field Dynamics and Bialgebras
• Quantum Groups and Polymer Quantum Mechanics