# Gandalf Lechner

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

** Abstract: **

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.