Charge conservation and the equivalence principle in noncommutative spacetime

Abstract

We investigate one of the consequences of the twisted Poincaré symmetry. We derive the charge conservation law and show that the equivalence principle is satisfied in the canonical noncommutative spacetime. We applied the twisted Poincaré symmetry to the Weinberg's analysis [11]. To this end, we generalize our earlier construction of the twisted S matrix [10], which apply the noncommutativity to the fourier modes, to the massless fields of integer spins. The transformation formula for the twisted S matrix for the massless fields of integer spin has been obtained. For massless fields of spin 1, we obtain the conservation of charge, and the universality of coupling constant for massless fields of spin 2, which can be interpreted as the equality of gravitational mass and inertial mass, i.e., the equivalence principle.