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Quantum mechanics, knot theory, and quantum doubles

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Abstract

In previous papers we have described quantum mechanics as a matrix symplectic geometry and showed the existence of a braiding and Hopf algebra structure behind our lattice quantum phase space. The first aim of this work is to give the defining commutation relations of the quantum Weyl-Schwinger-Heisenberg group associated with our ℜ-matrix solution. The second aim is to describe the knot formalism at work behind the matrix quantum mechanics. In this context, the quantum mechanics of a particle-antiparticle system (p¯p) moving in the quantum phase space is viewed as a quantum double.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Institut de Physique, Université d'Oran Es-sénia, 31100, Oran, Algeria

    A. E. F. Djemai

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  1. A. E. F. Djemai
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Djemai, A.E.F. Quantum mechanics, knot theory, and quantum doubles. Int J Theor Phys 35, 2029–2056 (1996). https://doi.org/10.1007/BF02302225

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  • DOI: https://doi.org/10.1007/BF02302225

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