Heat kernel coefficients for compact fuzzy spaces | Zendy

Naoki Sasakura | Zendy

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Heat kernel coefficients for compact fuzzy spaces

Author(s) -

Naoki Sasakura

Publication year - 2004

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2004/12/009

Subject(s) - heat kernel , mathematics , trace (psycholinguistics) , fuzzy logic , kernel (algebra) , asymptotic expansion , mathematical analysis , pure mathematics , computer science , artificial intelligence , philosophy , linguistics

I discuss the trace of a heat kernel Tr[e^(-tA)] for compact fuzzy spaces. Incontinuum theory its asymptotic expansion for t -> +0 provides geometricquantities, and therefore may be used to extract effective geometric quantitiesfor fuzzy spaces. For compact fuzzy spaces, however, an asymptotic expansionfor t -> +0 is not appropriate because of their finiteness. It is shown thateffective geometric quantities are found as coefficients of an approximatepower-law expansion of the trace of a heat kernel valid for intermediate valuesof t. An efficient method to obtain these coefficients is presented and appliedto some known fuzzy spaces to check its validity.Comment: Minor changes, 8 pages, 12 figures, LaTeX, JHEPclas

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