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E-raamat: Pinch Technique and its Applications to Non-Abelian Gauge Theories

, (Universitat de València, Spain), (University of California, Los Angeles)
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Pinch Technique and its Applications to Non-Abelian Gauge TheoriesSuurem pilt
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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.

Arvustused

"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

Muu info

Describes the Pinch Technique for constructing Green's functions for elementary particle theorists and graduate students.
Introduction: Why the pinch technique? xi
1 The pinch technique at one loop
1(44)
1.1 A brief history
1(2)
1.2 Notation and conventions
3(3)
1.3 The basic one-loop pinch technique
6(11)
1.4 Another way to the pinch technique
17(3)
1.5 Pinch technique vertices
20(11)
1.6 The pinch technique in the light-cone gauge
31(3)
1.7 The absorptive pinch technique construction
34(8)
1.8 Positivity and the pinch technique gluon propagator
42(3)
References
43(2)
2 Advanced pinch technique: Still one loop
45(30)
2.1 The pinch technique and the operator product expansion: Running mass and condensates
45(2)
2.2 The pinch technique and gauge-boson mass generation
47(15)
2.3 The pinch technique today: Background-field Feynman gauge
62(10)
2.4 What to expect beyond one loop
72(3)
References
73(2)
3 Pinch technique to all orders
75(11)
3.1 The s-t cancellation to all orders
75(4)
3.2 Quark-gluon vertex and gluon propagator to all orders
79(7)
References
85(1)
4 The pinch technique in the Batalin-Vilkovisky framework
86(18)
4.1 An overview of the Batalin-Vilkovisky formalism
88(5)
4.2 Examples
93(7)
4.3 Pinching in the Batalin-Vilkovisky framework
100(4)
References
102(2)
5 The gauge technique
104(10)
5.1 The original gauge technique for QED
105(3)
5.2 Massless longitudinal poles
108(1)
5.3 The gauge technique for NAGTs
109(5)
References
113(1)
6 Schwinger-Dyson equations in the pinch technique framework
114(30)
6.1 Lattice studies of gluon mass generation
115(2)
6.2 The need for a gauge-invariant truncation scheme for the Schwinger-Dyson equations of NAGTs
117(2)
6.3 The pinch technique algorithm for Schwinger-Dyson equations
119(1)
6.4 Pinch technique Green's functions from Schwinger-Dyson equations
120(11)
6.5 Solutions of the pinch technique Schwinger-Dyson equations and comparison with lattice data
131(3)
6.6 The QCD effective charge
134(10)
References
141(3)
7 Nonperturbative gluon mass and quantum solitons
144(23)
7.1 Notation
144(1)
7.2 Introduction
144(6)
7.3 The quantum solitons
150(2)
7.4 The center vortex soliton
152(15)
References
165(2)
8 Nexuses, sphalerons, and fractional topological charge
167(23)
8.1 Introduction to nexuses and junctions
167(3)
8.2 Nexuses in SU (N)
170(11)
8.3 The QCD sphaleron
181(5)
8.4 Chiral symmetry breakdown, nexuses, and fractional topological charge
186(4)
References
188(2)
9 A brief summary of d = 3 NAGTs
190(36)
9.1 Introduction
190(3)
9.2 Perturbative infrared instability
193(1)
9.3 The exact form of the zero-momentum effective action
193(4)
9.4 The dynamical gauge-boson mass
197(4)
9.5 The functional Schrodinger equation
201(8)
9.6 Dynamical gluon mass versus the Chern-Simons mass: Two phases
209(7)
9.7 Compactness and the Chern-Simons number of YMCS solitons
216(10)
References
223(3)
10 The pinch technique for electroweak theory
226(24)
10.1 General considerations
227(2)
10.2 The case of massless fermions
229(13)
10.3 Nonconserved currents and Ward identities
242(4)
10.4 The all-order construction
246(4)
References
248(2)
11 Other applications of the pinch technique
250(31)
11.1 Introduction
250(1)
11.2 Non-Abelian effective charges
250(5)
11.3 Physical renormalization schemes versus MS
255(1)
11.4 Gauge-independent off-shell form factors
256(7)
11.5 Resummation formalism for resonant transition amplitudes
263(7)
11.6 The pinch technique at finite temperature
270(1)
11.7 Basic principles of thermal field theory
271(5)
11.8 Hints of supersymmetry in the pinch technique Green's functions
276(5)
References
278(3)
Appendix: Feynman rules 281(4)
Index 285
John M. Cornwall's main research interest is non-perturbative quantum chromodynamics, both in four dimensions and in three (with applications to the functional Schrödinger equation and to high temperatures). Many of these results depend heavily on the pinch technique, as described in The Pinch Technique and its Applications to Non-Abelian Gauge Theories. He has also worked fairly recently on the applications of non-Abelian gauge theories to the early universe, in primordial magnetic fields and baryon asymmetry. Earlier work was in dynamical symmetry breaking, the equivalence theorem and effective potentials for gauge theories. He has also worked in space physics, including the aurora and Earth's ring current. Joannis Papavassiliou is a Researcher in the Department of Theoretical Physics and IFIC, the University of Valencia-CSIC. A large part of his work has been devoted to the development of the Pinch Technique, both its formal foundation as well as many applications, and he has published several articles on quantum field theory and particle phenomenology. Daniele Binosi is a Researcher at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT) and Fondazione Bruno Kessler. In addition to his work extending the Pinch Technique and its applications, he leads several policy-related European projects developing the vision and sustainability of quantum information foundations and technologies.
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