Electromagnetic and weak current operators for interacting systems within the front-form dynamics

Abstract

Electromagnetic and weak current operators for interacting systems should properly commute with the Poincar\'e generators and satisfy Hermiticity. The electromagnetic current should also satisfy ${\cal P}$ and ${\cal T}$ covariance and continuity equation. We show that in front-form dynamics the current can be constructed from auxiliary operators, defined in a Breit frame where initial and final three-momenta of the system are directed along the $z$ axis. Poincar\'e covariance constraints reduce for auxiliary operators to the ones imposed only by kinematical rotations around the $z$ axis; while Hermiticity requires a suitable behaviour of the auxiliary operators under rotations by $\pi$ around the $x$ or $y$ axes. Applications to deep inelastic structure functions and electromagnetic form factors are discussed. Elastic and transition form factors can be extracted without any ambiguity and in the elastic case the continuity equation is automatically satisfied, once Poincar\'e, ${\cal P}$ and ${\cal T}$ covariance, together with Hermiticity, are imposed.