Deformation quantization of principal bundles

@article{Aschieri2016DeformationQO,
  title={Deformation quantization of principal bundles},
  author={Paolo Aschieri},
  journal={International Journal of Geometric Methods in Modern Physics},
  year={2016},
  volume={13},
  pages={1630010}
}
  • P. Aschieri
  • Published 7 September 2016
  • Mathematics
  • International Journal of Geometric Methods in Modern Physics
We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles and, more in general, to the deformation of Hopf–Galois extensions. First, we twist deform the structure group in a quantum group, and this leads to a deformation of the fibers of the principal bundle. Next, we twist deform a subgroup of the group of automorphisms of the principal bundle, and this leads to a noncommutative base space… 

Gauge theory models on $\kappa$-Minkowski space: Results and prospects

Recent results obtained in κ-Poincaré invariant gauge theories on κ-Minkowski space are reviewed and commented. A Weyl quantization procedure can be applied to convolution algebras to derive a

References

SHOWING 1-10 OF 28 REFERENCES

Noncommutative Principal Bundles Through Twist Deformation

We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the

Principal Fibrations from Noncommutative Spheres

We construct noncommutative principal fibrations Sθ7→Sθ4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to

Noncommutative geometry and gravity

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of

Twisted Gauge Theories

Gauge theories on a space-time that is deformed by the Moyal–Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is

Noncommutative connections on bimodules and Drinfeld twist deformation

Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative

On generalized Hopf galois extensions

MODULI SPACES OF NON-COMMUTATIVE INSTANTONS: GAUGING AWAY NON-COMMUTATIVE PARAMETERS

Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere

Linear connections in non-commutative geometry

A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalization of the Leibniz rules of commutative geometry and uses the bimodule structure