LORENTZ INVARIANT AND SUPERSYMMETRIC INTERPRETATION OF NONCOMMUTATIVE QUANTUM FIELD THEORY

In this paper, using a Hopf-algebraic method, we construct deformed Poincaré SUSY algebra in terms of twisted (Hopf) algebra. By adapting this twist deformed super-Poincaré algebra as our fundamental symmetry, we can see the consistency between the algebra and non(anti)commutative relation among (super)coordinates and interpret that symmetry of non(anti)commutative QFT is in fact twisted one. The key point is validity of our new twist element that guarantees non(anti)commutativity of space. It is checked in this paper for [Formula: see text] case. We also comment on the possibility of noncommutative central charge coordinate. Finally, because our twist operation does not break the original algebra, we can claim that (twisted) SUSY is not broken in contrast to the string inspired [Formula: see text] SUSY in [Formula: see text] non(anti)commutative superspace.

DRINFELD TWIST FOR QUANTUM su(2) IN THE ADJOINT REPRESENTATION

We give a detailed description of the adjoint representation of Drinfeld's twist element, as well as its coproduct, for su q(2). We also discuss, as applications, the computation of the universal R-matrix in this representation and the problem of symmetrization of identical-particle states with quantum su(2) symmetry.