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SIGMA 6 (2010), 056, 12 pages arXiv:1003.5618
https://doi.org/10.3842/SIGMA.2010.056
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
Abstract
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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