Star products on generalised complex manifolds

Abstract

We regard classical phase space as a generalised complex manifold and analyse the B-transformation properties of the *-product of functions. The C*-algebra of smooth functions transforms in the expected way, while the C*-algebra of holomorphic functions (when it exists) transforms nontrivially. The B-transformed *-product encodes all the properties of phase-space quantum mechanics in the presence of a background magnetic field.

7 pages, refs added

References in corpus (9)

• Deformation quantization of Poisson manifolds, I
• Quantum Field Theory on Noncommutative Spaces
• Bound States Of Strings And $p$-Branes
• The Equivalence Postulate of Quantum Mechanics
• Symplectically Covariant Schrödinger Equation in Phase Space
• Dirac brackets from magnetic backgrounds
• Magnetic Backgrounds from Generalised Complex Manifolds
• Generalised Complex Geometry and the Planck Cone
• Noncommutative Manifolds from the Higgs Sector of Coincident D-Branes