Verfügbarkeit: The quantum theory of fields | Technische Universität München

The quantum theory of fields: 2 Modern applications

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Bibliographische Detailangaben
Beteilige Person:	Weinberg, Steven 1933-2021 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2005
Ausgabe:	Paperback ed.
Schlagwörter:	Quantenfeldtheorie Lehrbuch
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016258132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Umfang:	XXI, 489 S. Ill., graph. Darst.
ISBN:	9780521670548

Internformat

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adam_text	Contents Sections marked with an asterisk are somewhat out of the book s main line of development and may be omitted in a first reading. PREFACE TO VOLUME II xvii NOTATION xx 15 NON-ABELIAN GAUGE THEORIES 1 15.1 Gauge Invariance 2 Gauge transformations □ Structure constants □ Jacobi identity □ Adjoint repre¬ sentation G Yang-Mills theory □ Covariant derivatives □ Field strength tensor α Finite gauge transformations π Analogy with general relativity 15.2 Gauge Theory Lagrangians and Simple Lie Groups 7 Gauge field Lagrangian О Metric О Antisymmetric structure constants Π Simple, semisimple, and C/(l) Lie algebras □ Structure of gauge algebra □ Compact algebras □ Coupling constants 15.3 Field Equations and Conservation Laws 12 Conserved currents о Covariantly conserved currents □ Inhomogeneous field equations □ Homogeneous field equations □ Analogy with energy-momentum tensor ü Symmetry generators 15.4 Quantization 14 Primary and secondary first-class constraints □ Axial gauge О Gribov ambiguity о Canonical variables D Hamiltonian π Reintroduction of А® Π Covariant action D Gauge invariance of the measure 15.5 The De Witt-Faddeev-Popov Method 19 Generalization of axial gauge results о Independence of gauge fixing functionals □ Generalized Feynman gauge □ Form of vertices 15.6 Ghosts 24 Determinant as path integral О Ghost and antighost fields О Feynman rules for ghosts □ Modified action □ Power counting and renormalizability vii viii Contents 15.7 BRST Symmetry 27 Auxiliary field ha G BRST transformation □ Nilpotence □ Invariance of new action G BRST-cohomology □ Independence of gauge fixing D Application to electrodynamics D BRST-quantization □ Geometric interpretation 15.8 Generalizations of BRST Symmetry* 36 De Witt notation □ General Faddeev-Popov-De Witt theorem Π BRST transfor¬ mations □ New action Π Slavnov operator α Field-dependent structure constants G Generalized Jacobi identity G Invariance of new action G Independence of gauge fixing G Beyond quadratic ghost actions G BRST quantization □ BRST cohomology α Anti-BRST symmetry 15.9 The Batalin-Vilkovisky Formalism* 42 Open gauge algebras α Antifields α Master equation α Minimal fields and trivial pairs G BRST-transformations with antifields G Antibrackets G Anticanonical transformations G Gauge fixing G Quantum master equation Appendix A A Theorem Regarding Lie Algebras 50 Appendix В The Cartan Catalog 54 Problems 58 References 59 16 EXTERNAL FIELD METHODS 63 16.1 The Quantum Effective Action 63 Currents α Generating functional for all graphs G Generating functional for connected graphs G Legendre transformation G Generating functional for one- particle-irreducible graphs α Quantum-corrected field equations α Summing tree graphs 16.2 Calculation of the Effective Potential 68 Effective potential for constant fields G One loop calculation G Divergences G Renormalization G Fermion loops 16.3 Energy Interpretation 72 Adiabatic perturbation α Effective potential as minimum energy G Convexity α Instability between local minima G Linear interpolation 16.4 Symmetries of the Effective Action 75 Symmetry and renormalization G Slavnov-Taylor identities G Linearly realized symmetries G Fermionic fields and currents Problems 78 References 78 Contents ix 17 RENORMALIZATION OF GAUGE THEORIES 80 17.1 The Zinn-Justin Equation 80 Slavnov-Taylor identities for BRST symmetry □ External fields Kn(x) O An- tibrackets 17.2 Renormalization: Direct Analysis 82 Recursive argument □ BRST-symmetry condition on infinities □ Linearity in Kn(x) О New BRST symmetry α Cancellation of infinities □ Renormalization constants □ Nonlinear gauge conditions 17.3 Renormalization: General Gauge Theories* 91 Are non-renormalizable gauge theories renormalizable? D Structural constraints D Anticanonical change of variables □ Recursive argument G Cohomology theorems 17.4 Background Field Gauge 95 New gauge fixing functions D True and formal gauge invariance D Renormaliza¬ tion constants 17.5 A One-Loop Calculation in Background Field Gauge 100 One-loop effective action G Determinants D Algebraic calculation for constant background fields □ Renormalization of gauge fields and couplings □ Interpre¬ tation of infinities Problems 109 References 110 18 RENORMALIZATION GROUP METHODS 111 18.1 Where do the Large Logarithms Come From? 112 Singularities at zero mass О Infrared safe amplitudes and rates α Jets O Zero mass singularities from renormalization □ Renormalized operators 18.2 The Sliding Scale 119 Gell-Mann-Low renormalization □ Renormalization group equation Π One- loop calculations D Application to φ4 theory О Field renormalization factors D Application to quantum electrodynamics Π Effective fine structure constant D Field-dependent renormalized couplings □ Vacuum instability 183 Varieties of Asymptotic Behavior 130 Singularities at finite energy О Continued growth D Fixed point at finite coupling О Asymptotic freedom D Lattice quantization □ Triviality D Universal coefficients in the beta function χ Contents 18.4 Multiple Couplings and Mass Effects 139 Behavior near a fixed point о Invariant eigenvalues о Nonrenormalizable theories □ Finite dimensional critical surfaces □ Mass renormalization at zero mass □ Renormalization group equations for masses 18.5 Critical Phenomena* 145 Low wave numbers π Relevant, irrelevant, and marginal couplings G Phase transitions and critical surfaces □ Critical temperature D Behavior of correlation length D Critical exponent □ 4 — є dimensions D Wilson-Fisher fixed point Π Comparison with experiment Π Universality classes 18.6 Minimal Subtraction 148 Definition of renormalized coupling Π Calculation of beta function □ Applica¬ tion to electrodynamics □ Modified minimal subtraction D Non-renormalizable interactions 18.7 Quantum Chromodynamics 152 Quark colors and flavors □ Calculation of beta function G Asymptotic freedom □ Quark and gluon trapping α Jets G e+-e~~ annihilation into hadrons □ Accidental symmetries G Non-renormalizable corrections □ Behavior of gauge coupling π Experimental results for gs and Λ 18.8 Improved Perturbation Theory* 157 Leading logarithms G Coefficients of logarithms Problems 158 References 159 19 SPONTANEOUSLY BROKEN GLOBAL SYMMETRIES 163 19.1 Degenerate Vacua 163 Degenerate minima of effective potential G Broken symmetry or symmetric super¬ positions? Π Large systems □ Factorization at large distances G Diagonalization of vacuum expectation values D Cluster decomposition 19.2 Goldstone Bosons 167 Broken global symmetries imply massless bosons α Proof using effective potential α Proof using current algebra □ F factors and vacuum expectation values α Interactions of soft Goldstone bosons 19.3 Spontaneously Broken Approximate Symmetries 177 Pseudo-Goldstone bosons α Tadpoles α Vacuum alignment G Mass matrix Q Positivity Contents xi 19.4 Pions as Goldstone Bosons 182 SU{2) χ SU(2) chiral symmetry of quantum chromodynamics О Breakdown to isospin α Vector and axial-vector weak currents D Pion decay amplitude □ Axial form factors of nucleón D Goldberger-Treiman relation □ Vacuum alignment □ Quark and pion masses □ Soft pion interactions □ Historical note 19.5 Effective Field Theories: Pions and Nucléons 192 Current algebra for two soft pions □ Current algebra justification for effective Lagrangian D σ -model □ Transformation to derivative coupling Π Nonlinear realization of S 17(2) x S 17(2) □ Effective Lagrangian for soft pions Π Direct justification of effective Lagrangian □ General effective Lagrangian for pions □ Power counting □ Pion-pion scattering for massless pions Π Identification of jF-factor □ Pion mass terms in effective Lagrangian □ Pion-pion scattering for real pions □ Pion-pion scattering lengths D Pion-nucleon effective Lagrangian □ Covariant derivatives D gA φ 1 D Power counting with nucléons □ Pion-nucleon scattering lengths Π σ -terms Q Isospin violation □ Adler-Weisberger sum rule 19.6 Effective Field Theories: General Broken Symmetries 211 Transformation to derivative coupling D Goldstone bosons and right cosets □ Symmetric spaces □ Cartan decomposition D Nonlinear transformation rules □ Uniqueness D Covariant derivatives D Symmetry breaking terms D Application to quark mass terms □ Power counting О Order parameters 19.7 Effective Field Theories: SU(3) x S 17(3) 225 SU(3) multiplets and matrices Π Goldstone bosons of broken S 17(3) x S 17(3) □ Quark mass terms □ Pseudoscalar meson masses Π Electromagnetic corrections D Quark mass ratios D Higher terms in Lagrangian O Nucleón mass shifts 19.8 Anomalous Terms in Effective Field Theories* 234 Wess-Zumino-Witten term □ Five-dimensional form □ Integer coupling □ Uniqueness and de Rham cohomology 19.9 Unbroken Symmetries 238 Persistent mass conjecture □ Vafa-Witten proof о Small non-degenerate quark masses 19.10 The £7(1) Problem 243 Chiral Ł7(ł) symmetry О Implications for pseudoscalar masses Problems 246 References 247 xii Contents 20 OPERATOR PRODUCT EXPANSIONS 252 20.1 The Expansion: Description and Derivation 253 Statement of expansion О Dominance of simple operators О Path-integral deriva¬ tion 20.2 Momentum Flow* 255 φ2 contribution for two large momenta □ Renormalized operators D Integral equation for coefficient function □ φ2 contribution for many large momenta 20.3 Renormalization Gronp Equations for Coefficient Functions 263 Derivation and solution о Behavior for fixed points □ Behavior for asymptotic freedom 20.4 Symmetry Properties of Coefficient Functions 265 Invariance under spontaneously broken symmetries 20.5 Spectral Function Sum Rules 266 Spectral functions defined Π First, second, and third sum rules Q Application to dural SU(N) x SU(N) □ Comparison with experiment 20.6 Deep Inelastic Scattering 272 Form factors W and Wj □ Deep inelastic differential cross section □ Björken scaling o Parton model □ Callan-Gross relation О Sum rules □ Form factors Tt and Tj Π Relation between Tr and Wr О Symmetric tensor operators □ Twist D Operators of minimum twist ü Calculation of coefficient functions π Sum rules for parton distribution functions D Altarelli-Parisi differential equations □ Logarithmic corrections to Björken scaling 20.7 Renormalons* 283 Borei summation of perturbation theory π Instanton and renormalon obstruc¬ tions O Instantons in massless фА theory D Renormalons in quantum chromody- namics Appendix Momentum Flow: The General Case 288 Problems 292 References 293 21 SPONTANEOUSLY BROKEN GAUGE SYMMETRIES 295 21.1 Unitarity Gauge 295 Elimination of Goldstone bosons D Vector boson masses □ Unbroken symmetries and massless vector bosons π Complex representations О Vector field propagator О Continuity for vanishing gauge couplings Contents xiii 21.2 Renormalizable ^-Gauges 300 Gauge fixing function О Gauge-fixed Lagrangian □ Propagators 21.3 The Electroweak Theory 305 Lepton-number preserving symmetries D S 1/(2) χ U(l) □ W-, Z°, and photons □ Mixing angle D Lepton-vector boson couplings D W- and Z° masses D Muon decay D Effective fine structure constant О Discovery of neutral currents О Quark currents О Cabibbo angle □ с quark □ Third generation O Kobayashi-Maskawa matrix ü Discovery of W^ and Z° ü Precise experimental tests ü Accidental symmetries □ Nonrenormalizable corrections О Lepton nonconservation and neutrino masses □ Baryon nonconservation and proton decay 21.4 Dynamically Broken Local Symmetries* 318 Fictitious gauge fields G Construction of Lagrangian □ Power counting □ Gen¬ eral mass formula ü Example: SU(2) χ SU(2) G Custodial S U (2) x S U (2) D Technicolor 21.5 Electroweak-Strong Unification 327 Simple gauge groups Π Relations among gauge couplings G Renormalization group flow G Mixing angle and unification mass G Baryon and lepton noncon¬ servation 21.6 Superconductivity* 332 [/(1) broken to Z2 □ Goldstone mode G Effective Lagrangian D Conservation of charge G Meissner effect G Penetration depth G Critical field G Flux quan¬ tization G Zero resistance G ас Josephson effect G Landau-Ginzburg theory G Correlation length D Vortex lines G (7(1) restoration G Stability G Type I and II superconductors G Critical fields for vortices G Behavior near vortex center G Effective theory for electrons near Fermi surface G Power counting G Introduc¬ tion of pair field G Effective action Q Gap equation G Renormalization group equations G Conditions for superconductivity Appendix General Unitarity Gauge 352 Problemi; 353 References 354 22 ANOMALIES 359 22.1 The π° Decay Problem 359 Rate for π° —> 2y G Naive estimate G Suppression by chiral symmetry G Comparison with experiment 22.2 Transformation of tbe Measure: The Abelian Anomaly 362 Chiral and non-chiral transformations G Anomaly function G Chern-Pontryagin density G Nonconservation of current G Conservation of gauge-non-invariant xiv Contents current π Calculation of π° -> 2y □ Euclidean calculation D Atiyah-Singer index theorem 22.3 Direct Calculation of Anomalies: The General Case 370 Fermion non-conserving currents □ Triangle graph calculation D Shift vectors О Symmetric anomaly D Bardeen form Π Adler-Bardeen theorem □ Massive fermions □ Another approach Π Global anomalies 22.4 Anomaly-Free Gauge Theories 383 Gauge anomalies must vanish □ Real and pseudoreal representations G Safe groups Π Anomaly cancellation in standard model Π Gravitational anomalies □ Hypercharge assignments □ Another 17(1)? 22.5 Massless Bound States* 389 Composite quarks and leptons? □ Unbroken chiral symmetries □ t Hooft anomaly matching conditions α Anomaly matching for unbroken chiral SU(n) χ SU (η) with S U (N) gauge group Π The case I = 3OD Chiral St/(3) x SU{3) must be broken O t Hooft decoupling condition Π Persistent mass condition 22.6 Consistency Conditions 396 Wess-Zumino conditions Π BRST cohomology D Derivation of symmetric anomaly О Descent equations Π Solution of equations О Schwinger terms О Anomalies in Zinn- Justin equation □ Antibracket cohomology Π Algebraic proof of anomaly absence for safe groups 22.7 Anomalies and Goldstone Bosons 408 Anomaly matching □ Solution of anomalous Slavnov-Taylor identities □ Unique¬ ness о Anomalous Goldstone boson interactions D The case SU(3) x S 1/(3) □ Derivation of Wess-Zumino-Witten interaction □ Evaluation of integer coeffi¬ cient Q Generalization Problems 416 References 417 23 EXTENDED FIELD CONFIGURATIONS 421 23.1 The Uses of Topology 422 Topological classifications D Homotopy О Skyrmions D Derrick s theorem Π Domain boundaries □ Bogomoľnyi inequality α Cosmological problems α In¬ stantons D Monopoles and vortex lines □ Symmetry restoration 23.2 Homotopy Groups 430 Multiplication rule for % {Jt) D Associativity о Inverses D πι (Si) Π Topological conservation laws D Multiplication rule for nk(Ji) □ Winding number Contents xv 23.3 Monopoles 436 S 17(2)/[7(1) model Π Winding number D Electromagnetic field □ Magnetic monopole moment D Kronecker index D t Hooft-Polyakov monopole Π Another Bogomoľnyi inequality □ BPS monopole □ Dirac gauge G Charge quantization ü G/iH x t/(l)) monopoles D Cosmological problems □ Monopole-particle interactions □ G/H monopoles with G not simply connected D Irrelevance of field content 23.4 The Cartan-Maurer Integral Invariant 445 Definition of the invariant О Independence of coordinate system D Topological invariance Π Additivity О Integral invariant for Si >-*■ 1/(1) D Botťs theorem О Integral invariant for S3 h-» S 17(2) 23.5 Instantons 450 Evaluation of Cartan-Maurer invariant D Chern-Pontryagin density □ One more Bogomoľnyi inequality □ v = 1 solution α General winding number D Solution of U (I) problem D Baryon and lepton non-conservation by electroweak instantons ü Minkowskian approach □ Barrier penetration □ Thermal fluctuations 23.6 The Theta Angle 455 Cluster decomposition ü Superposition of winding numbers D P and CP non- conservation Π Complex fermion masses □ Suppression of Ρ and CP non- conservation by small quark masses О Neutron electric dipole moment □ Peccei- Quinn symmetry □ Axions D Axion mass O Axion interactions 23.7 Quantum Fluctuations around Extended Field Configurations 462 Fluctuations in general □ Collective parameters □ Determinental factor □ Cou¬ pling constant dependence □ Counting collective parameters 23.8 Vacuum Decay 464 False and true vacua О Bounce solutions D Four dimensional rotational invari¬ ance □ Sign of action D Decay rate per volume □ Thin wall approximation Appendix A Euclidean Path Integrals 468 Appendix В A List of Homotopy Groups 472 Problems 473 References 474 AUTHOR INDEX 478 SUBJECT INDEX 484 xvi Contents OUTLINE OF VOLUME I 1 HISTORICAL INTRODUCTION 2 RELATIVISTIC QUANTUM MECHANICS 3 SCATTERING THEORY 4 THE CLUSTER DECOMPOSITION PRINCIPLE 5 QUANTUM FIELDS AND ANTIPARTICLES 6 THE FEYNMAN RULES 7 THE CANONICAL FORMALISM 8 ELECTRODYNAMICS 9 PATH-INTEGRAL METHODS 10 NON-PERTURBATIVE METHODS 11 ONE-LOOP RADIATIVE CORRECTIONS IN QUANTUM ELECTRO¬ DYNAMICS 12 GENERAL RENORMALIZATION THEORY 13 INFRARED EFFECTS 14 BOUND STATES IN EXTERNAL FIELDS
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spellingShingle	Weinberg, Steven 1933-2021 The quantum theory of fields Quantenfeldtheorie (DE-588)4047984-5 gnd
subject_GND	(DE-588)4047984-5 (DE-588)4123623-3
title	The quantum theory of fields
title_auth	The quantum theory of fields
title_exact_search	The quantum theory of fields
title_full	The quantum theory of fields 2 Modern applications Steven Weinberg
title_fullStr	The quantum theory of fields 2 Modern applications Steven Weinberg
title_full_unstemmed	The quantum theory of fields 2 Modern applications Steven Weinberg
title_short	The quantum theory of fields
title_sort	the quantum theory of fields modern applications
topic	Quantenfeldtheorie (DE-588)4047984-5 gnd
topic_facet	Quantenfeldtheorie Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016258132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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