| Preface to Volume II |
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xvii | |
| Notation |
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xx | |
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Non-Abelian Gauge Theories |
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1 | (62) |
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2 | (5) |
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Finite gauge transformations |
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Analogy with general relativity |
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Gauge Theory Lagrangians and Simple Lie Groups |
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7 | (5) |
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Antisymmetric structure constants |
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Simple, semisimple, and U(1) Lie algebras |
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Structure of gauge algebra |
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Field Equations and Conservation Laws |
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12 | (2) |
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Covariantly conserved currents |
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Inhomogeneous field equations |
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Homogeneous field equations |
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Analogy with energy-momentum tensor |
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14 | (5) |
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Primary and secondary first-class constraints |
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Gauge invariance of the measure |
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The De Witt--Faddeev--Popov Method |
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19 | (5) |
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Generalization of axial gauge results |
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Independence of gauge fixing functionals |
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Generalized Feynman gauge |
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24 | (3) |
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Determinant as path integral |
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Ghost and antighost fields |
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Power counting and renormalizability |
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27 | (9) |
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Independence of gauge fixing |
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Application to electrodynamics |
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Generalizations of BRST Symmetry |
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36 | (6) |
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General Faddeev--Popov--De Witt theorem |
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Field-dependent structure constants |
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Generalized Jacobi identity |
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Independence of gauge fixing |
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Beyond quadratic ghost actions |
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The Batalin--Vilkovisky Formalism |
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42 | (21) |
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Minimal fields and trivial pairs |
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BRST-transformations with antifields |
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Anticanonical transformations |
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Appendix A A Theorem Regarding Lie Algebras |
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50 | (4) |
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Appendix B The Cartan Catalog |
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54 | (4) |
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58 | (1) |
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59 | (4) |
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63 | (17) |
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The Quantum Effective Action |
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63 | (5) |
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Generating functional for all graphs |
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Generating functional for connected graphs |
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Generating functional for one-particle-irreducible graphs |
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Quantum-corrected field equations |
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Calculation of the Effective Potential |
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68 | (4) |
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Effective potential for constant fields |
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72 | (3) |
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Effective potential as minimum energy |
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Instability between local minima |
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Symmetries of the Effective Action |
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75 | (5) |
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Symmetry and renormalization |
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Slavnov-Taylor identities |
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Linearly realized symmetries |
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Fermionic fields and currents |
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78 | (1) |
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78 | (2) |
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Renormalization of Gauge Theories |
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80 | (31) |
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80 | (2) |
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Slavnov--Taylor identities for BRST symmetry |
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Renormalization: Direct Analysis |
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82 | (9) |
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BRST-symmetry condition on infinities |
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Cancellation of infinities |
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Renormalization constants |
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Nonlinear gauge conditions |
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Renormalization: General Gauge Theories |
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91 | (4) |
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Are `non-renormalizable' gauge theories renormalizable? |
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Anticanonical change of variables |
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95 | (5) |
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New gauge fixing functions |
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True and formal gauge invariance |
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Renormalization constants |
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A One-Loop Calculation in Background Field Gauge |
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100 | (11) |
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One-loop effective action |
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Algebraic calculation for constant background fields |
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Renormalization of gauge fields and couplings |
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Interpretation of infinities |
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109 | (1) |
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110 | (1) |
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Renormalization Group Methods |
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111 | (52) |
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Where do the Large Logarithms Come From? |
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112 | (7) |
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Singularities at zero mass |
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`Infrared safe' amplitudes and rates |
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Zero mass singularities from renormalization |
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119 | (11) |
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Gell-Mann--Low renormalization |
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Renormalization group equation |
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Field renormalization factors |
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Application to quantum electrodynamics |
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Effective fine structure constant |
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Field-dependent renormalized couplings |
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Varieties of Asymptotic Behavior |
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130 | (9) |
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Singularities at finite energy |
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Fixed point at finite coupling |
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Universal coefficients in the beta function |
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Multiple Couplings and Mass Effects |
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139 | (6) |
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Behavior near a fixed point |
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Nonrenormalizable theories |
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Finite dimensional critical surfaces |
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Mass renormalization at zero mass |
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Renormalization group equations for masses |
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145 | (3) |
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Relevant, irrelevant, and marginal couplings |
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Phase transitions and critical surfaces |
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Behavior of correlation length |
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Wilson--Fisher fixed point |
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Comparison with experiment |
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148 | (4) |
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Definition of renormalized coupling |
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Calculation of beta function |
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Application to electrodynamics |
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Modified minimal subtraction |
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Non-renormalizable interactions |
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152 | (5) |
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Calculation of beta function |
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e+ -e- annihilation into hadrons |
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Non-renormalizable corrections |
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Behavior of gauge coupling |
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Experimental results for gs and Λ |
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Improved Perturbation Theory |
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157 | (6) |
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Coefficients of logarithms |
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158 | (1) |
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159 | (4) |
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Spontaneously Broken Global Symmetries |
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163 | (89) |
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163 | (4) |
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Degenerate minima of effective potential |
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Broken symmetry or symmetric superpositions? |
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Factorization at large distances |
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Diagonalization of vacuum expectation values |
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167 | (10) |
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Broken global symmetries imply massless bosons |
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Proof using effective potential |
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Proof using current algebra |
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F factors and vacuum expectation values |
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Interactions of soft Goldstone bosons |
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Spontaneously Broken Approximate Symmetries |
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177 | (5) |
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Pions as Goldstone Bosons |
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182 | (10) |
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SU(2) x SU(2) chiral symmetry of quantum chromodynamics |
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Vector and axial-vector weak currents |
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Axial form factors of nucleon |
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Goldberger-Treiman relation |
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Effective Field Theories: Pions and Nucleons |
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192 | (19) |
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Current algebra for two soft pions |
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Current algebra justification for effective Lagrangian |
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Transformation to derivative coupling |
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Nonlinear realization of SU(2) x SU(2) |
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Effective Lagrangian for soft pions |
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Direct justification of effective Lagrangian |
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General effective Lagrangian for pions |
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Pion--pion scattering for massless pions |
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Identification of F-factor |
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Pion mass terms in effective Lagrangian |
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Pion--pion scattering for real pions |
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Pion--pion scattering lengths |
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Pion--nucleon effective Lagrangian |
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Power counting with nucleons |
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Pion-nucleon scattering lengths |
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Adler--Weisberger sum rule |
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Effective Field Theories: General Broken Symmetries |
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211 | (14) |
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Transformation to derivative coupling |
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Goldstone bosons and right cosets |
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Nonlinear transformation rules |
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Application to quark mass terms |
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Effective Field Theories: SU(3) x SU(3) |
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225 | (9) |
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SU(3) multiplets and matrices |
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Goldstone bosons of broken SU(3) x SU(3) |
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Pseudoscalar meson masses |
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Electromagnetic corrections |
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Higher terms in Lagrangian |
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Anomalous Terms in Effective Field Theories |
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234 | (4) |
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Wess--Zumino--Witten term |
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Uniqueness and de Rham cohomology |
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238 | (5) |
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Persistent mass conjecture |
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Small non-degenerate quark masses |
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243 | (9) |
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Implications for pseudoscalar masses |
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246 | (1) |
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247 | (5) |
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Operator Product Expansions |
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252 | (43) |
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The Expansion: Description and Derivation |
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253 | (2) |
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Dominance of simple operators |
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255 | (8) |
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φ2 contribution for two large momenta |
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Integral equation for coefficient function |
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φ2 contribution for many large momenta |
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Renormalization Group Equations for Coefficient Functions |
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263 | (2) |
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Behavior for fixed points |
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Behavior for asymptotic freedom |
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Symmetry Properties of Coefficient Functions |
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265 | (1) |
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Invariance under spontaneously broken symmetries |
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Spectral Function Sum Rules |
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266 | (6) |
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Spectral functions defined |
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First, second, and third sum rules |
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Application to chiral SU(N) x SU(N) |
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Comparison with experiment |
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Deep Inelastic Scattering |
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272 | (11) |
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Deep inelastic differential cross section |
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Relation between Tr and Wr |
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Symmetric tensor operators |
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Operators of minimum twist |
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Calculation of coefficient functions |
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Sum rules for parton distribution functions |
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Altarelli--Parisi differential equations |
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Logarithmic corrections to Bjorken scaling |
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283 | (12) |
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Borel summation of perturbation theory |
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Instanton and renormalon obstructions |
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Instantons in massless φ4 theory |
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Renormalons in quantum chromodynamics |
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Appendix Momentum Flow: The General Case |
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288 | (4) |
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292 | (1) |
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293 | (2) |
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Spontaneously Broken Gauge Symmetries |
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295 | (64) |
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295 | (5) |
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Elimination of Goldstone bosons |
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Unbroken symmetries and massless vector bosons |
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Continuity for vanishing gauge couplings |
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300 | (5) |
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305 | (13) |
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Lepton-number preserving symmetries |
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Lepton-vector boson couplings |
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Effective fine structure constant |
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Discovery of neutral currents |
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Kobayashi--Maskawa matrix |
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Precise experimental tests |
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Nonrenormalizable corrections |
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Lepton nonconservation and neutrino masses |
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Baryon nonconservation and proton decay |
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Dynamically Broken Local Symmetries |
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318 | (9) |
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Construction of Lagrangian |
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Electroweak--Strong Unification |
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327 | (5) |
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Relations among gauge couplings |
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Renormalization group flow |
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Mixing angle and unification mass |
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Baryon and lepton nonconservation |
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332 | (27) |
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Type I and II superconductors |
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Critical fields for vortices |
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Behavior near vortex center |
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Effective theory for electrons near Fermi surface |
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Introduction of pair field |
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Renormalization group equations |
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Conditions for superconductivity |
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Appendix General Unitarity Gauge |
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352 | (1) |
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353 | (1) |
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354 | (5) |
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359 | (62) |
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359 | (3) |
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Suppression by chiral symmetry |
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Comparison with experiment |
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Transformation of the Measure: The Abelian Anomaly |
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362 | (8) |
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Chiral and non-chiral transformations |
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Chern--Pontryagin density |
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Nonconservation of current |
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Conservation of gauge-non-invariant current |
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Atiyah--Singer index theorem |
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Direct Calculation of Anomalies: The General Case |
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370 | (13) |
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Fermion non-conserving currents |
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Triangle graph calculation |
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Anomaly-Free Gauge Theories |
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383 | (6) |
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Gauge anomalies must vanish |
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Real and pseudoreal representations |
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Anomaly cancellation in standard model |
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389 | (7) |
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Composite quarks and leptons? |
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Unbroken chiral symmetries |
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't Hooft anomaly matching conditions |
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Anomaly matching for unbroken chiral SU(n) x SU(n) with SU(N) gauge group |
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Chiral SU(3) x SU(3) must be broken |
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't Hooft decoupling condition |
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Persistent mass condition |
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396 | (12) |
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Derivation of symmetric anomaly |
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Anomalies in Zinn-Justin equation |
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Algebraic proof of anomaly absence for safe groups |
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Anomalies and Goldstone Bosons |
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408 | (13) |
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Solution of anomalous Slavnov--Taylor identities |
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Anomalous Goldstone boson interactions |
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Derivation of Wess--Zumino--Witten interaction |
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Evaluation of integer coefficient |
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416 | (1) |
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417 | (4) |
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Extended Field Configurations |
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421 | (57) |
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422 | (8) |
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Topological classifications |
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Monopoles and vortex lines |
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430 | (6) |
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Multiplication rule for π1(M) |
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Topological conservation laws |
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Multiplication rule for πk(M) |
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436 | (9) |
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't Hooft--Polyakov monopole |
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Another Bogomol'nyi inequality |
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Monopole--particle interactions |
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G/H monopoles with G not simply connected |
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Irrelevance of field content |
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The Cartan--Maurer Integral Invariant |
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445 | (5) |
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Definition of the invariant |
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Independence of coordinate system |
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Integral invariant for S1 → U(1) |
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Integral invariant for S3 → SU(2) |
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450 | (5) |
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Evaluation of Cartan--Maurer invariant |
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Chern--Pontryagin density |
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One more Bogomol'nyi inequality |
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Baryon and lepton non-conservation by electroweak instantons |
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455 | (7) |
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Superposition of winding numbers |
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P and CP non-conservation |
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Suppression of P and CP non-conservation by small quark masses |
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Neutron electric dipole moment |
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Quantum Fluctuations around Extended Field Configurations |
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462 | (2) |
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Coupling constant dependence |
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Counting collective parameters |
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464 | (14) |
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Four dimensional rotational invariance |
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Appendix A Euclidean Path Integrals |
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468 | (4) |
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Appendix B A List of Homotopy Groups |
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472 | (1) |
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473 | (1) |
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474 | (4) |
| Author Index |
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478 | (6) |
| Subject Index |
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484 | |
Other versions by this Author
