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arXiv · hep-th/0306205

A Proposal for a Differential Calculus in Quantum Mechanics

E. Gozzi·M. Reuter
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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.

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E. Gozzi, M. Reuter. 2003-06-20. A Proposal for a Differential Calculus in Quantum Mechanics. https://doi.org/10.1142/s0217751x94000911

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