Fuzzy Complex Quadrics and Spheres

Details Fuzzy Complex Quadrics and Spheres Fuzzy Complex Quadrics and Spheres

2003-12-16

arxiv.org/abs/hep-th/0312190v1

JHEP 0402 (2004) 055

Physics

High Energy Physics

High Energy Physics - Theory

11 pages,typeset in LaTeX, uses yougtab.sty

Scientific paper

10.1088/1126-6708/2004/02/055

A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These matrix algebras contain the relevant degrees of freedom for describing truncations of harmonic expansions of functions on N-spheres. An Inonu-Wigner contraction of the quadric gives the co-tangent bundle to the commutative sphere in the continuum limit. It is shown how the degrees of freedom for the sphere can be projected out of a finite dimensional functional integral, using second-order Casimirs, giving a well-defined procedure for construction functional integrals over fuzzy spheres of any dimension.

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