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PUBDB-2022-07336

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png A proposal for a differential calculus in quantum mechanics

Gozzi, E. ; Reuter, M.

1994

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Please use a persistent id in citations: doi:10.3204/PUBDB-2022-07336

Report No.: DESY-93-061; UTS-DFT-93-10; hep-th/0306205

Abstract: In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics, we develop a {\it quantum-deformed} exterior calculus on the phase-space of an arbitrary hamiltonian system. Introducing additional bosonic and fermionic coordinates we construct a super-manifold which is closely related to the tangent and cotangent bundle over phase-space. Scalar functions on the super-manifold become equivalent to differential forms on the standard phase-space. The algebra of these functions is equipped with a Moyal super-star product which deforms the pointwise product of the classical tensor calculus. We use the Moyal bracket algebra in order to derive a set of quantum-deformed rules for the exterior derivative, Lie derivative, contraction, and similar operations of the Cartan calculus.

Keyword(s): quantum mechanics ; operator: algebra ; algebra: deformation ; differential forms ; Hamiltonian formalism ; supersymmetry

Note: Theorie

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Contributing Institute(s):

1. DESY Retrocat (DESY(-2012))

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

Experiment(s):

1. No specific instrument

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article Gozzi, E. ; Reuter, M.
A proposal for a differential calculus in quantum mechanics
International journal of modern physics / A 09(13), 2191 - 2227 (1994) [10.1142/S0217751X94000911]1994     Files BibTeX | EndNote: XML, Text | RIS

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