Holdings: The quantum theory of fields

The quantum theory of fields: 2 Modern applications

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Bibliographic Details
Main Author:	Weinberg, Steven 1933-2021 (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2010
Edition:	10th pr.
Subjects:	Quantenfeldtheorie Lehrbuch
Online Access:	Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XXI, 489 S. Ill., graph. Darst.
ISBN:	9780521670548 9780521550024

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MARC


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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 Π Structure constants Q Jacobi identity О Adjoint repre¬ sentation Π Yang-Mills theory □ Covariant derivatives D Field strength tensor О Finite gauge transformations □ Analogy with general relativity 15.2 Gauge Theory Lagrangians and Simple Lie Groups 7 Gauge field Lagrangian Π Metric D Antisymmetric structure constants D Simple, semisimple, and 1/(1) Lie algebras D Structure of gauge algebra О Compact algebras Π Coupling constants 153 Field Equations and Conservation Laws 12 Conserved currents О Covariantly conserved currents D Inhomogeneous field equations □ Homogeneous field equations □ Analogy with energy-momentum tensor D Symmetry generators 15.4 Quantization 14 Primary and secondary first-class constraints □ Axial gauge o Gribov ambiguity О Canonical variables ü Hamiltonian G Reintroduction of A°x □ Covariant action О Gauge invariance of the measure 15.5 The De Witt-Faddeev-Popov Method 19 Generalization of axial gauge results D Independence of gauge fixing functionals α Generalized Feynman gauge D Form of vertices 15.6 Ghosts 24 Determinant as path integral D Ghost and antighost fields Π Feynman rules for ghosts α Modified action Q Power counting and renormalizability vii viii Contents 15.7 BRST Symmetry 27 Auxiliary field hx □ BRST transformation О Nilpotence О Invariance of new action D BRST-cohomology О Independence of gauge fixing □ Application to electrodynamics О BRST-quantization α Geometric interpretation 15.8 Generalizations of BRST Symmetry* 36 De Witt notation О General Faddeev-Popov-De Witt theorem D BRST transfor¬ mations О New action О Slavnov operator G Field-dependent structure constants D Generalized Jacobi identity ü Invariance of new action О Independence of gauge fixing D Beyond quadratic ghost actions D BRST quantization О BRST cohomology O Anti-BRST symmetry 15.9 The Batalin-Vilkovisky Formalism* 42 Open gauge algebras D Antifields D Master equation О Minimal fields and trivial pairs □ BRST-transformations with antifields О Antibrackets Q Anticanonical transformations □ Gauge fixing о 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 ü Generating functional for all graphs D Generating functional for connected graphs D Legendre transformation О Generating functional for one- particle-irreducible graphs D Quantum-corrected field equations О Summing tree graphs 16.2 Calculation of the Effective Potential 68 Effective potential for constant fields Π One loop calculation □ Divergences О Renormalization O Fermion loops 163 Energy Interpretation 72 Adiabatic perturbation О Effective potential as minimum energy D Convexity о Instability between local minima О Linear interpolation 16.4 Symmetries of the Effective Action 75 Symmetry and renormalization □ Slavnov-Taylor identities □ Linearly realized symmetries Π 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 О External fields Kn(x) □ An- tibrackets 17.2 Renormalization: Direct Analysis 82 Recursive argument D BRST-symmetry condition on infinities О Linearity in К„(х) □ New BRST symmetry D Cancellation of infinities π Renormalization constants π Nonlinear gauge conditions 173 Renormalization: General Gauge Theories* 91 Are non-renormalizable gauge theories renormalizable? D Structural constraints о Anticanonical change of variables О Recursive argument □ Cohomology theorems 17.4 Background Field Gauge 95 New gauge fixing functions О True and formal gauge invariance □ Renormaliza¬ tion constants 175 A One-Loop Calculation in Background Field Gauge 100 One-loop effective action α Determinants О 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 O Jets O Zero mass singularities from renormalization ü Renormalized operators 18.2 The Sliding Scale 119 Gell-Mann-Low renormalization О Renormalization group equation □ One- loop calculations D Application to φ* theory О Field renormalization factors О Application to quantum electrodynamics О Effective fine structure constant Π Field-dependent renormaiized couplings □ Vacuum instability 183 Varieties of Asymptotic Behavior 130 Singularities at finite energy □ Continued growth О Fixed point at finite coupling □ Asymptotic freedom D Lattice quantization G Triviality □ Universal coefficients in the beta function x Contents 18.4 Multiple Couplings and Mass Effects 139 Behavior near a fixed point О Invariant eigenvalues D Nonrenormalizable theories G Finite dimensional critical surfaces D Mass renormalization at zero mass □ Renormalization group equations for masses 18.5 Critical Phenomena* 145 Low wave numbers D Relevant, irrelevant, and marginal couplings D Phase transitions and critical surfaces D Critical temperature π Behavior of correlation length □ Critical exponent Q 4 — є dimensions α Wilson-Fisher fixed point Q Comparison with experiment □ Universality classes 18.6 Minimal Subtraction 148 Definition of renormalized coupling О Calculation of beta function □ Applica¬ tion to electrodynamics ü Modified minimal subtraction О Non-renormalizable interactions 18.7 Quantum Chromodynamics 152 Quark colors and flavors G Calculation of beta function Q Asymptotic freedom G Quark and gluon trapping Π Jets Q e+-e~ annihilation into hadrons G Accidental symmetries G Non-renormalizable corrections G Behavior of gauge coupling G Experimental results for g5 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? D Large systems G Factorization at large distances G Diagonalization of vacuum expectation values G Cluster decomposition 19.2 Goldstone Bosons 167 Broken global symmetries imply massless bosons G Proof using effective potential □ Proof using current algebra G F factors and vacuum expectation values D Interactions of soft Goldstone bosons 193 Spontaneously Broken Approximate Symmetries 177 Pseudo-Goldstone bosons α Tadpoles α Vacuum alignment G Mass matrix G Positivity Contents xi 19.4 Pions as Goldstone Bosons 182 SU(2) x S 1/(2) chiral symmetry of quantum chromodynamics D Breakdown to isospin D Vector and axial-vector weak currents D Pion decay amplitude D Axial form factors of nucleón Π Goldberger-Treiman relation D 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 О Current algebra justification for effective Lagrangian Π σ -model о Transformation to derivative coupling ü Nonlinear realization of S U( 2) x S 1/(2) Π Effective Lagrangian for soft pions o Direct justification of effective Lagrangian Π General effective Lagrangian for pions □ Power counting D Pion-pion scattering for massless pions D Identification of / -factor D Pion mass terms in effective Lagrangian □ Pion-pion scattering for real pions o Pion-pion scattering lengths □ Pion-nucleon effective Lagrangian ü Covariant derivatives D gA φ 1 D Power counting with nucléons α Pion-nucleon scattering lengths D σ -terms О Isospin violation О 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 α Cartan decomposition о Nonlinear transformation rules О Uniqueness □ Covariant derivatives О Symmetry breaking terms Q Application to quark mass terms ü Power counting ü Order parameters 19.7 Effective Field Theories: SU(3) x SU(3) 225 S 1/(3) multiplets and matrices α Goldstone bosons of broken S 1/(3) x SU(3) D Quark mass terms D Pseudoscalar meson masses О Electromagnetic corrections О Quark mass ratios О Higher terms in Lagrangian D Nucleón mass shifts 19.8 Anomalous Terms in Effective Field Theories* 234 Wess-Zumino-Witten term О Five-dimensional form □ Integer coupling Π Uniqueness and de Rham cohomology 19.9 Unbroken Symmetries 238 Persistent mass conjecture □ Vafa-Witten proof □ Small non-degenerate quark masses 19.10 The ř/(l) Problem 243 Chiral 1/(1) 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 G Path-integral deriva¬ tion 20.2 Momentum Flow* 255 φ2 contribution for two large momenta D Renormalized operators О Integral equation for coefficient function Ο φ2 contribution for many large momenta 203 Renormalization Group Equations for Coefficient Functions 263 Derivation and solution О Behavior for fixed points D Behavior for asymptotic freedom 20.4 Symmetry Properties of Coefficient Functions 265 Invariance under spontaneously broken symmetries 203 Spectral Function Sum Rules 266 Spectral functions defined D First, second, and third sum rules D Application to chiral SU(N) χ SU(N) G Comparison with experiment 20.6 Deep Inelastic Scattering 272 Form factors Wi and Wi О Deep inelastic differential cross section o Björken scaling D Parton model D Callan-Gross relation О Sum rules ü Form factors T and T2 □ Relation between Tr and Wr D Symmetric tensor operators □ Twist Π Operators of minimum twist D Calculation of coefficient functions ü Sum rules for parton distribution functions О Altarelli-Parisi differential equations D Logarithmic corrections to Björken scaling 20.7 Renormalons* 283 Borei summation of perturbation theory о Instanton and renormalon obstruc¬ tions D Instantons in massless φ* theory □ 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 Gange 295 Elimination of Goldstone bosons α Vector boson masses α Unbroken symmetries and massless vector bosons G Complex representations G Vector field propagator О Continuity for vanishing gauge couplings Contents xiii 21.2 Renormalizable ¿-Gauges 300 Gauge fixing function О Gauge-fixed Lagrangian □ Propagators 213 The Electroweak Theory 305 Lepton-number preserving symmetries π SU(2) χ t/(l) Π W±, Z°, and photons О Mixing angle □ Lepton-vector boson couplings D W- and Z° masses О Muon decay О Effective fine structure constant О Discovery of neutral currents □ Quark currents □ Cabibbo angle □ с quark □ Third generation D Kobayashi-Maskawa matrix о Discovery of W± and Z° D Precise experimental tests о Accidental symmetries D Nonrenormalizable corrections □ Lepton nonconservation and neutrino masses D Baryon nonconservation and proton decay 21.4 Dynamically Broken Local Symmetries 318 Fictitious gauge fields О Construction of Lagrangian D Power counting О Gen¬ eral mass formula О Example: S 17(2) χ SU(2) G Custodial SU(2) χ SU (2) О Technicolor 21.5 Electroweak-Strong Unification 327 Simple gauge groups □ Relations among gauge couplings D Renormalization group flow Π Mixing angle and unification mass □ Baryon and lepton noncon¬ servation 21.6 Superconductivity 332 1/(1) broken to Z.2 О Goldstone mode D Effective Lagrangian D Conservation of charge О Meissner effect О Penetration depth О Critical field O Flux quan¬ tization о Zero resistance π ас Josephson effect □ Landau-Ginzburg theory о Correlation length D Vortex lines □ 1/(1) restoration о Stability о Type I and II superconductors D Critical fields for vortices О Behavior near vortex center ü Effective theory for electrons near Fermi surface Π Power counting Π Introduc¬ tion of pair field D Effective action Π Gap equation D Renormalization group equations О Conditions for superconductivity Appendix General Unitarity Gauge 352 Problems 353 References 354 22 ANOMALIES 359 22.1 The π Decay Problem 359 Rate for π° -♦ 2y О Naive estimate D Suppression by chiral symmetry □ Comparison with experiment 212 Transformation of the Measure: The Abelian Anomaly 362 Chiral and non-chiral transformations α Anomaly function ü Chern-Pontryagin density Π Nonconservation of current D Conservation of gauge-non-invariant xiv Contents current D Calculation of π° -» 2y α Euclidean calculation O Atiyah-Singer index theorem 223 Direct Calculation of Anomalies: The General Case 370 Fermion non-conserving currents D Triangle graph calculation □ Shift vectors D Symmetric anomaly D Bardeen form O Adler-Bardeen theorem □ Massive fermions D Another approach ü Global anomalies 214 Anomaly-Free Gauge Theories 383 Gauge anomalies must vanish D Real and pseudoreal representations □ Safe groups Π Anomaly cancellation in standard model D Gravitational anomalies □ Hypercharge assignments G Another 1/(1)? 225 Massless Bound States* 389 Composite quarks and leptons? □ Unbroken chiral symmetries □ t Hooft anomaly matching conditions D Anomaly matching for unbroken chiral S U (ή) χ SV(n) with SU(N) gauge group D The case N = 3 D G Chiral SU(3) χ SC/(3) must be broken G t Hooft decoupling condition G Persistent mass condition 22.6 Consistency Conditions 396 Wess-Zumino conditions G BRST cohomology G Derivation of symmetric anomaly G Descent equations G Solution of equations G Schwinger terms G Anomalies in Zinn-Justin equation G Antibracket cohomology □ Algebraic proof of anomaly absence for safe groups 22.7 Anomalies and Goldstone Bosons 408 Anomaly matching G Solution of anomalous Slavnov-Taylor identities G Unique¬ ness D Anomalous Goldstone boson interactions G The case SC/(3) x S 1/(3) G Derivation of Wess-Zumino- Witten interaction G Evaluation of integer coeffi¬ cient G Generalization Problems 416 References 417 23 EXTENDED FIELD CONFIGURATIONS 421 23.1 The Uses of Topology 422 Topological classifications G Homotopy G Skyrmions α Derrick s theorem G Domain boundaries G Bogomoľnyi inequality D Cosmological problems □ In- stantons G Monopoles and vortex lines G Symmetry restoration 23.2 Homotopy Groups 430 Multiplication rule for п (Л) G Associativity D Inverses G πι (Si) O Topological conservation laws G Multiplication rule for nt(Jf) G Winding number Contents xv 23.3 Monopoles 436 SU(2)/U(l) model О Winding number D Electromagnetic field D Magnetic monopole moment □ Kronecker index □ t Hooft-Polyakov monopole D Another Bogomoľnyi inequality π BPS monopole G Dirac gauge □ Charge quantization О G /{H χ 1/(1)) monopoles □ Cosmological problems О Monopole-particle interactions D G/H monopoles with G not simply connected О Irrelevance of field content 23.4 The Cartan-Maurer Integral Invariant 445 Definition of the invariant D Independence of coordinate system O Topological invariance D Additivity О Integral invariant for Si ·—► 1/(1) □ Bott s theorem α Integral invariant for S3 *-» SU(2) 23.5 Instantons 450 Evaluation of Cartan-Maurer invariant D Chern-Pontryagin density О One more Bogomoľnyi inequality D v = 1 solution D General winding number D Solution of 1/(1) problem D Baryon and lepton non-conservation by electroweak instantons G Minkowskian approach G Barrier penetration G Thermal fluctuations 23.6 The Theta Angle 455 Cluster decomposition G Superposition of winding numbers α Ρ and CP non- conservation G Complex fermion masses G Suppression of Ρ and CP non- conservation by small quark masses G Neutron electric dipole moment D Peccei- Quinn symmetry G Axions G Axion mass G Axion interactions 23.7 Quantum Fluctuations around Extended Field Configurations 462 Fluctuations in general G Collective parameters G Determinental factor G Cou¬ pling constant dependence G Counting collective parameters 23.8 Vacuum Decay 464 False and true vacua G Bounce solutions G Four dimensional rotational invari¬ ance G Sign of action G Decay rate per volume G 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
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spelling	Weinberg, Steven 1933-2021 Verfasser (DE-588)11562855X aut The quantum theory of fields 2 Modern applications Steven Weinberg 10th pr. Cambridge [u.a.] Cambridge Univ. Press 2010 XXI, 489 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenfeldtheorie (DE-588)4047984-5 s DE-604 (DE-604)BV010519919 2 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020776868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
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=020776868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010519919
work_keys_str_mv	AT weinbergsteven thequantumtheoryoffields2

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