Spectral triples and Toeplitz operators

Published 13 Feb 2014 in math-ph and math.MP | (1402.3061v1)

Abstract: We give examples of spectral triples, in the sense of A. Connes, constructed using the algebra of Toeplitz operators on smoothly bounded strictly pseudoconvex domains in $C^n$, or the star product for the Berezin-Toeplitz quantization. Our main tool is the theory of generalized Toeplitz operators on the boundary of such domains, due to Boutet de Monvel and Guillemin.

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