Noncommutative field theories from a deformation point of view
arXiv:0710.2140
Abstract
In this review we discuss the global geometry of noncommutative field theories from a deformation point of view: The space-times under consideration are deformations of classical space-time manifolds using star products. Then matter fields are encoded in deformation quantizations of vector bundles over the classical space-time. For gauge theories we establish a notion of deformation quantization of a principal fiber bundle and show how the deformation of associated vector bundles can be obtained.
19 pages. Contribution to the Proceedings of the Leipzig Conference "Recent Developments in Quantum Field Theory"
References in corpus (12)
- Deformation quantization of Poisson manifolds, I
- The quantum structure of spacetime at the Planck scale and quantum fields
- Nonabelian noncommutative gauge theory via noncommutative extra dimensions
- Noncommutative Yang-Mills from equivalence of star products
- Noncommutative gauge theory for Poisson manifolds
- Strong Connections and Chern-Connes Pairing in the Hopf-Galois Theory
- The characteristic classes of Morita equivalent star products on symplectic manifolds
- Variations on deformation quantization
- Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups
- A C*-Algebraic Model for Locally Noncommutative Spacetimes
- The Picard groupoid in deformation quantization
- Rigidity of K-theory under deformation quantization