Eur. Phys. J. C 70, 479-489 (2010)
https://doi.org/10.1140/epjc/s10052-010-1440-1

The algebra of physical observables in non-linearly realized gauge theories

¹ Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Strasse 3, 79104, Freiburg, Germany
² Phys. Dept., University of Milan, via Celoria 16, 20133, Milan, Italy

andrea.quadri@mi.infn.it

Received: 3 August 2010
Published online: 30 September 2010

Abstract

We classify the physical observables in spontaneously broken non-linearly 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 non-linearly 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.