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

Describes the Pinch Technique for constructing Green's functions for elementary particle theorists and graduate students.

John M. Cornwall (Author), Joannis Papavassiliou (Author), Daniele Binosi (Author)

9780521437523, Cambridge University Press

Hardback, published 23 December 2010

304 pages, 73 b/w illus.
25.4 x 17.9 x 2 cm, 0.73 kg

"The authors are authorities in the field. Cornwall is the person who introduced the pinch techniques in the late 1970's; Papavassiliou and Binosi did most of their research in this field. Nobody knows this matter better than the authors."
Giuseppe Nardelli, Mathematical Reviews

Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's 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 Green's 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.

Introduction
1. The Pinch Technique at one loop
2. Advanced pinch technique – still one loop
3. Pinch technique to all orders
4. The pinch technique in the Batalin-Vilkovisky framework
5. The gauge technique
6. Schwinger-Dyson equations in the pinch technique framework
7. Non-perturbative gluon mass and quantum solitons
8. Nexuses, sphalerons, and fractional topological charge
9. A brief summary of d=3 NAGTs
10. The pinch technique for electroweak theory
11. Other applications of the pinch technique
Appendix
Index.

Subject Areas: Mathematical physics [PHU], Particle & high-energy physics [PHP], Nuclear physics [PHN], Theoretical & mathematical astronomy [PGC]