Noncommutative Topological Quantum Field Theory, Noncommutative Floer Homology, Noncommutative Hodge Theory
Abstract
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT) and Noncommutative Floer Homology (NCFH). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we present some "Noncommutative" Versions of Hodge Theory for noncommutative differentail forms and tangential cohomology for foliations.
Keywords
Cite
@article{arxiv.1401.4080,
title = {Noncommutative Topological Quantum Field Theory, Noncommutative Floer Homology, Noncommutative Hodge Theory},
author = {Ioannis P. Zois},
journal= {arXiv preprint arXiv:1401.4080},
year = {2014}
}
Comments
31 pages. Extended version of two talks presented during the International Conference on Mathematical Modeling in Physical Sciences, 1-5 September 2013, Prague, Czech Republic