Pinch Technique: Theory and Applications

TL;DR

The paper reviews the Pinch Technique's theoretical foundations and diverse applications in non-Abelian gauge theories, emphasizing gauge independence, Ward identities, and its extension to non-perturbative QCD and electroweak sectors.

Contribution

It provides a comprehensive overview of the PT, including its diagrammatic formulation, generalization to theories with spontaneous symmetry breaking, and its all-order and non-perturbative extensions.

Findings

Derivation of gauge-independent Green's functions in QCD

Connection between PT and Background Field Method

Application of PT to define gauge-invariant form factors

Abstract

We review the theoretical foundations and most important physical applications of the Pinch Technique (PT). This method allows the construction of off-shell Green's functions in non-Abelian gauge theories that are independent of the gauge-fixing parameter and satisfy ghost-free Ward identities. We first present the diagrammatic formulation of the technique in QCD, deriving at one loop the gauge independent gluon self-energy, quark-gluon vertex, and three-gluon vertex, together with their Abelian Ward identities. The generalization to theories with spontaneous symmetry breaking is carried out in detail, and the connection with the optical theorem and the dispersion relations are explained within the electroweak sector of the Standard Model. The equivalence between the PT and the Feynman gauge of the Background Field Method (BFM) is elaborated, and the crucial differences between the two methods are critically scrutinized. The Batalin-Vilkovisky quantization method and the general formalism of algebraic renormalization are introduced, and the all-order generalization of the PT is thoroughly examined. The extension of the PT to the non-perturbative domain of the QCD Schwinger-Dyson equations is presented systematically, and the main advantages of the resulting self-consistent truncation scheme are discussed. A plethora of physical applications relying on the PT are reviewed, such as the definition of gauge-independent off-shell form-factors, the construction of non-Abelian effective charges, the gauge-invariant treatment of resonant transition amplitudes and unstable particles, and the dynamical generation of an effective gluon mass.