Gandalf Lechner

Star products and deformation procedures in quantization, non- commutative geometry and quantum field theory


In this lecture I will discuss several examples of star products and deformations of algebras together with their applications to a number of physical problems. At first, it will be shown how the algebra of observables of a system of classical mechanics undergoes a star produc tdeformation when the system is quantized. We will then discuss a generalization of this structure, namely the class of deformations (of C*-algebras) introduced by Rieffel. Examples for such Rieffel deformations can be found in non-commutative geometry and quantum field theory on non-commutative spaces, such as the non-commutative torus, the Moyal plane, or Wightman theories on the non-commutative Minkowski space. This lecture also serves as a guide from the point of view of non-commutative geometry / star product deformation towards the topic of constructions of quantum field theories by deformations, which will be addressed in Summers' talk on Friday.