The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories

TL;DR

This paper classifies physical observables in nonlinearly realized gauge theories using a loopwise expansion governed by Weak Power-Counting, employing the BV formalism to analyze quantum deformations and compare with linear realizations.

Contribution

It introduces a classification method for observables in nonlinear gauge theories using the WPC and BV formalism, extending the understanding of quantum deformations and renormalization.

Findings

Dependence of vertex functional on Goldstone fields via canonical transformation.

WPC condition allows Weinberg relation to hold at tree level.

Comparison shows WPC is less restrictive than strict renormalizability.

Abstract

We classify the physical observables in spontaneously broken nonlinearly realized gauge theories in the recently proposed loopwise expansion governed by the Weak Power-Counting (WPC) and the Local Functional Equation. The latter controls the non-trivial quantum deformation of the classical nonlinearly realized gauge symmetry, to all orders in the loop expansion. The Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the vertex functional on the Goldstone fields is obtained via a canonical transformation w.r.t. the BV bracket associated with the BRST symmetry of the model. We also compare the WPC with strict power-counting renormalizability in linearly realized gauge theories. In the case of the electroweak group we find that the tree-level Weinberg relation still holds if power-counting renormalizability is weakened to the WPC condition.