Symmetry and Dynamics of Quantum Field Theories on Noncommutative Spaces
Helsinki University, Finland.
The underlying symmetries of noncommutative field theories together with their implications are analyzed. In particular, the concept of a noncommutative field based on the interplay between twisted Poincare symmetry and residual symmetry of the Lorentz group is formulated. Various general dynamical arguments supporting this construction, such as the light-wedge causality condition and the integrability condition for Tomonaga-Schwinger equation, are presented. The use of the twist procedure for the formulation of noncommutative gauge field theories is critically considered. Some problems still to be solved are proposed.