Gauge invariance in the presence of a cutoff

Understand

We use the method of gauging equations to construct the electromagnetic current operator for the two-nucleon system in a theory with a finite cutoff.

• The employed formulation ensures that the two-nucleon T-matrix and corresponding five-point function, in the cutoff theory, are identical to the ones formally defined by a reference theory without a cutoff.
• A feature of our approach is that it effectively introduces a cutoff into the reference theory in a way that maintains the long-range part of the exchange current operator; for applications to effective field theory (EFT), this property is usually sufficient to guarantee the predictive power of the resulting cutoff theory.
• In addition, our approach leads to Ward-Takahashi (WT) identities that are linear in the interactions.