Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Introduction: Why the pinch technique? -- A quick outline of the book -- Some uses of the pinch technique -- Constructing pinch technique Green's functions and equations -- 1 The pinch technique at one loop -- 1.1 A brief history -- 1.2 Notation and conventions -- 1.3 The basic one-loop pinch technique -- 1.3.1 Origin of the longitudinal momenta -- 1.3.2 The basic pinch operation -- 1.3.3 The pinch technique gluon self-energy at one loop -- 1.4 Another way to the pinch technique -- 1.4.1 Process independence -- 1.4.2 Intrinsic pinch technique -- 1.5 Pinch technique vertices -- 1.5.1 The one-loop pinch technique quark-gluon vertex and its Ward identity -- 1.5.2 The one-loop, three-gluon vertex and its Ward identity -- 1.5.3 The four-gluon vertex -- 1.6 The pinch technique in the light-cone gauge -- 1.7 The absorptive pinch technique construction -- 1.7.1 The strong version of the optical theorem -- 1.7.2 The fundamental s-t cancellation -- 1.8 Positivity and the pinch technique gluon propagator -- References -- 2 Advanced pinch technique: Still one loop -- 2.1 The pinch technique and the operator product expansion: Running mass and condensates -- 2.2 The pinch technique and gauge-boson mass generation -- 2.2.1 General remarks -- 2.2.2 Dynamical gauge-boson mass generation in QCD -- 2.2.3 The need for dynamical mass in d=2+1 QCD -- 2.2.4 What do vertices and propagators look like when dynamical mass is generated? -- 2.2.5 Mass generation through Higgs-Kibble-Goldstone fields -- 2.3 The pinch technique today: Background-field Feynman gauge -- 2.3.1 The effective action -- 2.3.2 The background-field method for gauge fields -- 2.3.3 Pinch technique and background Feynman gauge correspondence -- 2.3.4 The generalized pinch technique.

2.4 What to expect beyond one loop -- References -- 3 Pinch technique to all orders -- 3.1 The s-t cancellation to all orders -- 3.2 Quark-gluon vertex and gluon propagator to all orders -- References -- 4 The pinch technique in the Batalin-Vilkovisky framework -- 4.1 An overview of the Batalin-Vilkovisky formalism -- 4.1.1 Green's functions: Conventions -- 4.1.2 The Batalin-Vilkovisky formalism -- 4.2 Examples -- 4.2.1 Slavnov-Taylor identities -- 4.2.2 Background-quantum identities -- 4.2.3 Closed expressions for auxiliary functions -- 4.2.4 A special case: The (background) Landau gauge -- 4.3 Pinching in the Batalin-Vilkovisky framework -- References -- 5 The gauge technique -- 5.1 The original gauge technique for QED -- 5.1.1 Scalar QED -- 5.1.2 Fermionic QED -- 5.2 Massless longitudinal poles -- 5.3 The gauge technique for NAGTs -- 5.3.1 The gauge technique in the light-cone gauge -- References -- 6 Schwinger-Dyson equations in the pinch technique framework -- 6.1 Lattice studies of gluon mass generation -- 6.2 The need for a gauge-invariant truncation scheme for the Schwinger-Dyson equations of NAGTs -- 6.3 The pinch technique algorithm for Schwinger-Dyson equations -- 6.4 Pinch technique Green's functions from Schwinger-Dyson equations -- 6.4.1 First step:… -- 6.4.2 Second step:… -- 6.4.3 Third step:… -- 6.4.4 The final rearrangement and the new Schwinger-Dyson equation -- 6.4.5 Truncation of the pinch technique Schwinger-Dyson equation -- 6.5 Solutions of the pinch technique Schwinger-Dyson equations and comparison with lattice data -- 6.6 The QCD effective charge -- 6.6.1 The prototype: The QED effective charge -- 6.6.2 The QCD effective charge -- References -- 7 Nonperturbative gluon mass and quantum solitons -- 7.1 Notation -- 7.2 Introduction -- 7.2.1 Condensates and solitons -- 7.2.2 What does confinement really mean?.

7.3 The quantum solitons -- 7.4 The center vortex soliton -- 7.4.1 The standard Abelian center vortex -- 7.4.2 The general center vortex -- 7.4.3 The Q-matrices and the center-vortex homotopy -- 7.4.4 Confinement -- 7.4.5 Screening -- 7.4.6 Hybrids -- References -- 8 Nexuses, sphalerons, and fractional topological charge -- 8.1 Introduction to nexuses and junctions -- 8.1.1 Junctions -- 8.1.2 Nexuses, magnetic charge, and topological charge -- 8.2 Nexuses in SU(N) -- 8.2.1 The SU(2) nexus -- 8.2.2 The SU(N) nexus -- 8.2.3 Nexus magnetic charge -- 8.2.4 Topological charge as an intersection number for nonorientable vortex surfaces -- 8.3 The QCD sphaleron -- 8.3.1 The QCD sphaleron as a d=3 object -- 8.3.2 Sphalerons in four-dimensional Minkowski space -- 8.4 Chiral symmetry breakdown, nexuses, and fractional topological charge -- References -- 9 A brief summary of d=3 NAGTs -- 9.1 Introduction -- 9.2 Perturbative infrared instability -- 9.3 The exact form of the zero-momentum effective action -- 9.3.1 The effective action and the pinch technique -- 9.4 The dynamical gauge-boson mass -- 9.4.1 Early pinch technique work -- 9.4.2 One-loop gap equations and lattice simulations -- 9.5 The functional Schrodinger equation -- 9.5.1 The gauge technique and the FSE -- 9.5.2 The proposed infrared-effective action -- 9.6 Dynamical gluon mass versus the Chern-Simons mass: Two phases -- 9.6.1 The nonperturbative phase uncovered by the pinch technique -- 9.6.2 YMCS solitons -- 9.7 Compactness and the Chern-Simons number of YMCS solitons -- 9.7.1 Sphalerons, knots, and compactness -- References -- 10 The pinch technique for electroweak theory -- 10.1 General considerations -- 10.2 The case of massless fermions -- 10.2.1 The unitary gauge -- 10.2.2 Absorptive construction in the electroweak sector.

10.2.3 Background field method away from xi Q=1: physical versus unphysical thresholds -- 10.3 Nonconserved currents and Ward identities -- 10.4 The all-order construction -- References -- 11 Other applications of the pinch technique -- 11.1 Introduction -- 11.2 Non-Abelian effective charges -- 11.2.1 Electroweak effective charges -- 11.2.2 Relation to physical cross sections -- 11.3 Physical renormalization schemes versus MS -- 11.4 Gauge-independent off-shell form factors -- 11.4.1 Neutrino charge radius -- 11.5 Resummation formalism for resonant transition amplitudes -- 11.5.1 An example -- 11.6 The pinch technique at finite temperature -- 11.7 Basic principles of thermal field theory -- 11.7.1 The pinch technique in the zero-Matsubara-frequency sector -- 11.7.2 Developments in the full thermal field theory -- 11.8 Hints of supersymmetry in the pinch technique Green's functions -- References -- Appendix 1: Feynman rules -- A.1 Rxi and BFM gauges -- A.2 Antifields -- A.3 BFM sources -- Index.