Dynamical origin of the -noncommutativity in field theory from quantum mechanics

2006/02/04 by M. Rosenbaum, Marcos Rosenbaum, J. David Vergara +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1016/j.physleta.2006.01.071

published as Phys.Lett.A354:389-395,2006 · 17 pages, to be published in Phys. Lett. A

openalex publication_date 2006/02/04 · arxiv created 2006/04/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that introducing an extended Heisenberg algebra in the context of the Weyl-Wigner-Groenewold-Moyal formalism leads to a deformed product of the classical dynamical variables that is inherited to the level of quantum field theory, and that allows us to relate the operator space noncommutativity in quantum mechanics to the quantum group inspired algebra deformation noncommutativity in field theory.

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• Canonical quantization, spacetime noncommutativity and deformed symmetries in field theory
• On deformed quantum mechanical schemes and ★-value equations based on the space-space noncommutative Heisenberg-Weyl group
• Noncommutative field theory from quantum mechanical space–space noncommutativity