Spectral triples and Toeplitz operators

2014/02/13 by Englis, M., Falk, K., Iochum, B.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1402.3061

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 Cⁿ, 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.

Related

• Spectral Triples and Generalized Crossed Products
• Spectral properties of semi-classical Toeplitz operators
• Semi-classical spectral asymptotics of Toeplitz operators on strictly pseudodonvex domains
• Algebraic Properties of Toeplitz operators on the symmetrized polydisk
• A Class of Toeplitz Operators in Several Complex Variables