Splitting Ward identity

Understand

Within the background-field framework we present a path integral derivation of the splitting Ward identity for the one-particle irreducible effective action in the presence of an infrared regulator, and make connection with earlier works on the subject.

• The approach is general in the sense that it does not rely on how the splitting is performed.
• This identity is then used to address the problem of background dependence of the effective action at an arbitrary energy scale.
• We next introduce the modified master equation and emphasize its role in constraining the effective action.