A Natural Basis for Spinor and Vector Fields on the Noncommutative sphere

Abstract

The product of two Heisenberg-Weil algebras contains the Jordan-Schwinger representation of su(2). This Algebra is quotiented by the square-root of the Casimir to produce a non-associative algebra denoted by $\Psi$. This algebra may be viewed as the right-module over one of its associative subalgebras which corresponds to the algebra of scalar fields on the noncommutative sphere. It is now possible to interpret other subspaces as the space of spinor or vector fields on the noncommutative sphere. A natural basis of $\Psi$ is given which may be interpreted as the deformed entries in the rotation matrices of SU(2).

21 pages Latex, No figures. Submitted to Journal of Mathematical Physics

References in corpus (5)

• Topologically nontrivial field configurations in noncommutative geometry
• Field Theory on a Supersymmetric Lattice
• Chirality and Dirac Operator on Noncommutative Sphere
• A Natural Basis of States for the Noncommutative Sphere and its Moyal bracket
• Non Commutative Differential Geometry, and the Matrix Representations of Generalised Algebras