On the Wilsonian renormalization group equation for nuclear current operators

TL;DR

This paper solves the Wilsonian RG equation for nuclear current operators, introducing a new cutoff independence condition that ensures current conservation despite a modified Ward-Takahashi identity.

Contribution

It provides a novel solution to the Wilsonian RG equation for nuclear currents, clarifying the ambiguity and establishing a modified Ward-Takahashi identity.

Findings

Effective current operator obeys a modified Ward-Takahashi identity

Ensures cutoff independence of the two-body Green function with current insertion

Maintains current conservation despite modifications

Abstract

We present the solution to the recently derived Wilsonian renormalization group (RG) equation for nuclear current operators. In order to eliminate the present ambiguity in the RG equation itself, we introduce a new condition specifying the cutoff independence of the five point Green function corresponding to the two-body propagator with current operator insertion. The resulting effective current operator is then shown to obey a modified Ward-Takahashi identity which differs from the usual one, but that nevertheless leads to current conservation.