Fuzzy Complex Quadrics and Spheres

Dolan, Brian and O'Connor, Denjoe and Presnajder, Peter (2004) Fuzzy Complex Quadrics and Spheres. Journal of High Energy Physics, 0402.

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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.

Item Type: Article
Keywords: Field Theories in Higher Dimensions Differential and Algebraic Geometry Non-Commutative Geometry
Academic Unit: Faculty of Science and Engineering > Experimental Physics
Item ID: 247
Depositing User: Dr. Brian Dolan
Date Deposited: 30 Aug 2005
Journal or Publication Title: Journal of High Energy Physics
Publisher: IOP
Refereed: Yes

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