The interface of noncommutative geometry and physics
arXiv:hep-th/0206007
Abstract
The progress of noncommutative geometry has been crucially influenced, from the beginning, by quantum physics: we review this development in recent years. The Standard Model, with its central role for the Dirac operator, led to several formulations culminating in the concept of a real spectral triple. String theory then came into contact with NCG, leading to an emphasis on Moyal-like algebras and formulations of quantum field theory on noncommutative spaces. Hopf algebras have yielded an unexpected link between the noncommutative geometry of foliations and perturbative quantum field theory. The quest for a suitable foundation of quantum gravity continues to promote fruitful ideas, among them the spectral action principle and the search for a better understanding of "noncommutative spaces".
Latex, 15 pages, talk given at the 6th Conference on Clifford Algebras and Applications, Cookeville, TN, May 2002
References in corpus (18)
- Noncommutative Perturbative Dynamics
- Gravity coupled with matter and foundation of non-commutative geometry
- Hopf Algebras, Renormalization and Noncommutative Geometry
- The Spectral Action Principle
- D-branes and Deformation Quantization
- Hopf algebras, cyclic cohomology and the transverse index theory
- Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
- On the unitarity problem in space/time noncommutative theories
- Algebras of distributions suitable for phase-space quantum mechanics. I
- A Short Survey of Noncommutative Geometry
- The Standard Model as a noncommutative geometry: the low energy regime
- Chiral Gauge Anomalies on Noncommutative R^4
- Time-ordered Perturbation Theory on Noncommutative Spacetime: Basic Rules
- String Geometry and the Noncommutative Torus
- Quantum symmetry groups of noncommutative spheres
- On summability of distributions and spectral geometry
- Generalized Yang-Mills actions from Dirac operator determinants
- Wave-Function renormalization and the Hopf algebra of Connes and Kreimer