Symmetries in noncommutative field theories: Hopf versus Lie

Abstract

I discuss motivations for introducing Hopf algebra symmetries in noncommutative field theories and briefly describe twisting of main symmetry transformations. New results include an extended list of twisted gauge invariants (which may help to overcome the problem of inconsistency of equations of motion) and a gauge-covariant twist operator (leading to a gauge-covariant star product).

based on talk at at the Workshop on Quantum Field Theory and Representation Theory, Sao Paulo, August 21-24, 2007