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Heat kernel coefficients for compact fuzzy spaces

Naoki Sasakura
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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.

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Naoki Sasakura. 2004-12-27. Heat kernel coefficients for compact fuzzy spaces. https://doi.org/10.1088/1126-6708%2F2004%2F12%2F009

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