Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 056, 12 pages      arXiv:1003.5618
Contribution to the Special Issue “Noncommutative Spaces and Fields”

A Note on Dirac Operators on the Quantum Punctured Disk

Slawomir Klimek and Matt McBride
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN 46202, USA

Received March 30, 2010, in final form July 07, 2010; Published online July 16, 2010

We study quantum analogs of the Dirac type operator −2z∂/∂z on the punctured disk, subject to the Atiyah-Patodi-Singer boundary conditions. We construct a parametrix of the quantum operator and show that it is bounded outside of the zero mode.

Key words: operator theory; functional analysis; non-commutative geometry.

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