Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
Quantum Algebra
2012-02-21 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We present several results on the geometry of the quantum projective plane CP2q. They include: explicit generators for the K-theory and the K-homology; a real calculus with a Hodge star operator; anti-selfdual connections on line bundles with explicit computation of the corresponding 'monopoles' and 'instanton' charges; complete diagonalization of gauged Laplacians on these line bundles; quantum invariants via equivariant K-theory and q-indices.
Cite
@article{arxiv.0903.3551,
title = {Anti-selfdual Connections on the Quantum Projective Plane: Monopoles},
author = {Francesco D'Andrea and Giovanni Landi},
journal= {arXiv preprint arXiv:0903.3551},
year = {2012}
}
Comments
dcpic, pdflatex. v2: 51 pages. Added a Section of Concluding remarks, an Appendix on representations of the coordinate algebra of the quantum projective plane and three additional references. Several minor changes throughout the paper including changes in terminology. To appear in CMP.