Abstract. I discuss the trace of a heat kernel Tr(e^−tA) for compact fuzzy spaces. In continuum theory its asymptotic expansion for t→+0 provides geometric quantities, and therefore may be used to extract effective geometric quantities for fuzzy spaces. For compact fuzzy spaces, however, an asymptotic expansion for t→+0 is not appropriate because of their finiteness. It is shown that effective geometric quantities are found as coefficients of an approximate power-law expansion of the trace of a heat kernel valid for intermediate values of t. An efficient method to obtain these coefficients is presented and applied to some known fuzzy spaces to check its validity.

Key words: Lattice Quantum Field Theory; Lattice Models of Gravity; Non-Commutative Geometry

E-print number: hep-th/0411029
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Received 9 November 2004, accepted for publication 3 December 2004
Published 3 January 2005