Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-06-20
Int.J.Mod.Phys. A9 (1994) 2191-2228
Physics
High Energy Physics
High Energy Physics - Theory
TeX file with phyzzx macro, 43 pages, no figures
Scientific paper
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.
Gozzi Ennio
Reuter Martin
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