Eur. Phys. J. Plus (2021) 136: 695
https://doi.org/10.1140/epjp/s13360-021-01665-9

Regular Article

Background field method and generalized field redefinitions in effective field theories

INFN, Sezione di Milano, via Celoria 16, 20133, Milano, Italy

^a andrea.quadri@mi.infn.it

Received: 4 March 2021
Accepted: 10 June 2021
Published online: 28 June 2021

Abstract

We show that in a spontaneously broken effective gauge field theory, quantized in a general background $R_{\xi }$-gauge, also the background fields undergo a non-linear (albeit background-gauge invariant) field redefinition induced by radiative corrections. This redefinition proves to be crucial in order to renormalize the coupling constants of gauge-invariant operators in a gauge-independent way. The classical background-quantum splitting is also in general non-linearly deformed (in a non gauge-invariant way) by radiative corrections. Remarkably, such deformations vanish in the Landau gauge, to all orders in the loop expansion.