Noncommutative field theories from a deformation point of view

Understand

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.