Covariant and single-field effective action with the background-field formalism

Understand

In the context of scalar quantum field theory we introduce a class of generically nonlinear quantum-background splits for which the splitting Ward identity, encoding the single field dependence in the effective action, can be solved exactly.

• We show that this can be used to construct an effective action which is both covariant and dependent on the background and fluctuation fields only through a single total field in a way independent from the dynamics.
• Moreover we discuss the criteria under which the ultraviolet symmetries are inherited by the quantum effective action.
• The approach is demonstrated through some examples, including the $O(N)$ effective field theory, which might be of interest for the Higgs sector of the Standard Model or its extensions.