Pinch Technique: Theory and Applications

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.

245 pages, 92 figures

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• The Gluon Propagator without lattice Gribov copies on a finer lattice
• Gauge and Scheme Dependence of Mixing Matrix Renormalization
• On One-Loop Gap Equations for the Magnetic Mass in d=3 Gauge Theory
• The Pinch Technique at Two Loops
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• Gauge Dependence of Mass and Condensate in Chirally Asymmetric Phase of Quenched QED3
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• Infrared finite ghost propagator in the Feynman gauge
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• SU_L(2) X U_Y(1)-invariant description of the bilepton contribution to the WWV vertex in the minimal 331 model
• The QCD Effective Charge to All Orders
• Electroweak pinch technique to all orders
• Two-loop next-to-leading $\mt$ corrections to the $\rho$ parameter
• The Laplacian Gauge Gluon Propagator in SU(N_c)
• Application of the Pinch Technique to Neutral Current Amplitudes and the Concept of the Z Mass
• Chiral-logarithmic Corrections to the S and T Parameters in Higgsless Models
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• Nonperturbative QCD, gauge-fixing, Gribov copies, and the lattice
• Gauge-independent Thermal $\beta$ Function In Yang-Mills Theory
• DIAGRAMMATIC ANALYSIS OF QCD GAUGE TRANSFORMATIONS AND GAUGE CANCELLATIONS
• The Two-Loop Pinch Technique in the Electroweak Sector
• Gauge-Independent Off-Shell Fermion Self-Energies at Two Loops: The Cases of QED and QCD
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• Two-loop electroweak corrections to the $\rho$ parameter beyond the leading approximation
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• Gauge-independent resummed gluon self-energy in hot QCD
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• One-loop Corrections to the S Parameter in the Four-site Model
• The influence of Gribov copies on the gluon and ghost propagator
• Asymptotic properties of Born-improved amplitudes with gauge bosons in the final state

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