Deformed symmetries in noncommutative field theories

Abstract

In this lecture we discuss the problem of symmetries in noncommutative field theories. The twist approach is used to derive deformed symmetries. In this approach the algebra of symmetry generators remains undeformed, but the Leibniz rules for the generators change. We give some examples. In the case of the canonically deformed space the twisted Poincare symmetry is analyzed and the problem of nonconserved charges is discussed. A way to overcome this problem is to introduce a dynamical noncommutativity and we briefly describe it.