The Pinch Technique and its Applications to Non-Abelian Gauge Theories

Non-Abelian gauge theories such as quantum chromodynamics (QCD) or electroweak theory are best studied with the aid of Greens functions that are gauge-invariant off-shell but unlike for the photon in quantum electrodynamics conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Greens functions and has many useful applications. Beginning with elementary one-loop examples this book goes on to extend the method to all orders showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived and used to show how a dynamical gluon mass arises in QCD. Applications are given to the center vortex picture of confinement the gauge-invariant treatment of resonant amplitudes the definition of non-Abelian effective charges high-temperature effects and even supersymmetry. This book is ideal for elementary particle theorists and graduate students.