Amazon cover image
Image from Amazon.com

Gauge Field Theories.

By: Series: Cambridge Monographs on Mathematical PhysicsPublisher: Cambridge : Cambridge University Press, 2000Copyright date: ©2000Edition: 2nd edDescription: 1 online resource (631 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511151200
Subject(s): Genre/Form: Additional physical formats: Print version:: Gauge Field TheoriesDDC classification:
  • 530.14/35
LOC classification:
  • QC793.3.F5 -- P65 2000eb
Online resources:
Contents:
Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- 0 Introduction -- 0.1 Gauge invariance -- 0.2 Reasons for gauge theories of strong and electroweak interactions -- QCD -- Electroweak theory -- 1 Classical fields, symmetries and their breaking -- 1.1 The action, equations of motion, symmetries and conservation laws -- Equations of motion -- Global symmetries -- Space-time transformations -- Examples -- 1.2 Classical field equations -- Scalar field theory and spontaneous breaking of global symmetries -- Spinor fields -- 1.3 Gauge field theories -- U(1) gauge symmetry -- Non-abelian gauge symmetry -- 1.4 From classical to quantum fields (canonical quantization) -- Scalar fields -- The Feynman propagator -- Spinor fields -- Symmetry transformations for quantum fields -- 1.5 Discrete symmetries -- Space reflection -- Time reversal -- Charge conjugation -- Summary and the CPT transformation -- CP violation in the neutral… -- Problems -- 2 Path integral formulation of quantum field theory -- 2.1 Path integrals in quantum mechanics -- Transition matrix elements as path integrals -- Matrix elements of position operators -- 2.2 Vacuum-to-vacuum transitions and the imaginary time formalism -- General discussion -- Harmonic oscillator -- Euclidean Green's functions -- 2.3 Path integral formulation of quantum field theory -- Green's functions as path integrals -- Action quadratic in fields -- Gaussian integration -- 2.4 Introduction to perturbation theory -- Perturbation theory and the generating functional -- Wick's theorem -- An example: four-point Green's function in LambdaPhi -- Momentum space -- 2.5 Path integrals for fermions -- Grassmann algebra -- Anticommuting c-numbers -- Dirac propagator.
2.6 Generating functionals for Green's functions and proper vertices -- effective potential -- Classification of Green's functions and generating functionals -- Effective action -- Spontaneous symmetry breaking and effective action -- Effective potential -- 2.7 Green's functions and the scattering operator -- Problems -- 3 Feynman rules for Yang-Mills theories -- 3.1 The Faddeev-Popov determinant -- Gauge invariance and the path integral -- Faddeev-Popov determinant -- Examples -- Non-covariant gauges -- 3.2 Feynman rules for QCD -- Calculation of the Faddeev-Popov determinant -- Feynman rules -- 3.3 Unitarity, ghosts, Becchi-Rouet-Stora transformation -- Unitarity and ghosts -- BRS and anti-BRS symmetry -- Problems -- 4 Introduction to the theory of renormalization -- 4.1 Physical sense of renormalization and its arbitrariness -- Bare and 'physical' quantities -- Counterterms and the renormalization conditions -- Arbitrariness of renormalization -- Final remarks -- 4.2 Classification of the divergent diagrams -- Structure of the UV divergences by momentum power counting -- Classification of divergent diagrams -- Necessary counterterms -- 4.3 LambdaPhi: low order renormalization -- Feynman rules including counterterms -- Calculation of Fig. 4.8(b) -- Comments on analytic continuation to… -- Lowest order renormalization -- 4.4 Effective field theories -- Problems -- 5 Quantum electrodynamics -- 5.1 Ward-Takahashi identities -- General derivation by the functional technique -- Examples -- 5.2 Lowest order QED radiative corrections by the dimensional regularization technique -- General introduction -- Vacuum polarization -- Electron self-energy correction -- Electron self-energy: IR singularities regularized by photon mass -- On-shell vertex correction -- 5.3 Massless QED -- 5.4 Dispersion calculation of O(Alpha) virtual corrections in massless QED….
Self-energy calculation -- Vertex calculation -- 5.5 Coulomb scattering and the IR problem -- Corrections of order Alpha -- IR problem to all orders in Alpha -- Problems -- 6 Renormalization group -- 6.1 Renormalization group equation (RGE) -- Derivation of the RGE -- Solving the RGE -- Green's functions for rescaled momenta -- RGE in QED -- 6.2 Calculation of the renormalization group functions Beta, Gamma, Gamma -- 6.3 Fixed points -- effective coupling constant -- Fixed points -- Effective coupling constant -- 6.4 Renormalization scheme and gauge dependence of the RGE parameters -- Renormalization scheme dependence -- Effective Alpha in QED -- Gauge dependence of the Beta-function -- Problems -- 7 Scale invariance and operator product expansion -- 7.1 Scale invariance -- Scale transformations -- Dilatation current -- Conformal transformations -- 7.2 Broken scale invariance -- General discussion -- Anomalous breaking of scale invariance -- 7.3 Dimensional transmutation -- 7.4 Operator product expansion (OPE) -- Short distance expansion -- Light-cone expansion -- 7.5 The relevance of the light-cone -- Electron-positron annihilation -- Deep inelastic hadron leptoproduction -- Wilson coefficients and moments of the structure function -- 7.6 Renormalization group and OPE -- Renormalization of local composite operators -- RGE for Wilson coefficients -- OPE beyond perturbation theory -- 7.7 OPE and effective field theories -- Problems -- 8 Quantum chromodynamics -- 8.1 General introduction -- Renormalization and BRS invariance -- counterterms -- Asymptotic freedom of QCD -- The Slavnov-Taylor identities -- 8.2 The background field method -- 8.3 The structure of the vacuum in non-abelian gauge theories -- Homotopy classes and topological vacua -- Physical vacuum -- Theta-vacuum and the functional integral formalism.
8.4 Perturbative QCD and hard collisions -- Parton picture -- Factorization theorem -- 8.5 Deep inelastic electron-nucleon scattering in first order QCD (Feynman gauge) -- Structure functions and Born approximation -- Deep inelastic quark structure functions in the first order in the strong coupling constant -- Final result for the quark structure functions -- Hadron structure functions -- probabilistic interpretation -- 8.6 Light-cone variables, light-like gauge -- 8.7 Beyond the one-loop approximation -- Comments on the IR problem in QCD -- Problems -- 9 Chiral symmetry -- spontaneous symmetry breaking -- 9.1 Chiral symmetry of the QCD lagrangian -- 9.2 Hypothesis of spontaneous chiral symmetry breaking in strong interactions -- 9.3 Phenomenological chirally symmetric model of the strong interactions (Sigma-model) -- 9.4 Goldstone bosons as eigenvectors of the mass matrix and poles of Green's functions in theories with elementary scalars -- Goldstone bosons as eigenvectors of the mass matrix -- General proof of Goldstone's theorem -- 9.5 Patterns of spontaneous symmetry breaking -- 9.6 Goldstone bosons in QCD -- 10 Spontaneous and explicit global symmetry breaking -- 10.1 Internal symmetries and Ward identities -- Preliminaries -- Ward identities from the path integral -- Comparison with the operator language -- Ward identities and short-distance singularities of the operator products -- Renormalization of currents -- 10.2 Quark masses and chiral perturbation theory -- Simple approach -- Approach based on use of the Ward identity -- 10.3 Dashen's theorems -- Formulation of Dashen's theorems -- Dashen's conditions and global symmetry broken by weak gauge interactions -- 10.4 Electromagnetic… -- Electromagnetic… -- Spectral function sum rules -- Results -- 11 Higgs mechanism in gauge theories -- 11.1 Higgs mechanism.
11.2 Spontaneous gauge symmetry breaking by radiative corrections -- 11.3 Dynamical breaking of gauge symmetries and vacuum alignment -- Dynamical breaking of gauge symmetry -- Examples -- Problems -- 12 Standard electroweak theory -- 12.1 The lagrangian -- 12.2 Electroweak currents and physical gauge boson fields -- 12.3 Fermion masses and mixing -- 12.4 Phenomenology of the tree level lagrangian -- Effective four-fermion interactions -- Z couplings -- 12.5 Beyond tree level -- Renormalization and counterterms -- Corrections to gauge boson propagators -- Fermion self-energies -- Running Alpha(µ) in the electroweak theory -- Muon decay in the one-loop approximation -- Corrections to the Z partial decay widths -- 12.6 Effective low energy theory for electroweak processes -- QED as the effective low energy theory -- 12.7 Flavour changing neutral-current processes -- QCD corrections to CP violation in the neutral kaon system -- Problems -- 13 Chiral anomalies -- 13.1 Triangle diagram and different renormalization conditions -- Introduction -- Calculation of the triangle amplitude -- Different renormalization constraints for the triangle amplitude -- Important comments -- 13.2 Some physical consequences of the chiral anomalies -- Chiral invariance in spinor electrodynamics -- Pi… -- Chiral anomaly for the axial U(1) current in QCD… -- Anomaly cancellation in the SU(2) × U(1) electroweak theory -- Anomaly-free models -- 13.3 Anomalies and the path integral -- Introduction -- Abelian anomaly -- Non-abelian anomaly and gauge invariance -- Consistent and covariant anomaly -- 13.4 Anomalies from the path integral in Euclidean space -- Introduction -- Abelian anomaly with Dirac fermions -- Non-abelian anomaly and chiral fermions -- Problems -- 14 Effective lagrangians -- 14.1 Non-linear realization of the symmetry group -- Non-linear Sigma-model.
Effective lagrangian in the….
Summary: An expanded and up-dated book examining gauge theories and their symmetries.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF000390
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP000390
Ebrary Ebrary Sudan Available
Ebrary Ebrary Tunisia Available
Total holds: 0

Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- 0 Introduction -- 0.1 Gauge invariance -- 0.2 Reasons for gauge theories of strong and electroweak interactions -- QCD -- Electroweak theory -- 1 Classical fields, symmetries and their breaking -- 1.1 The action, equations of motion, symmetries and conservation laws -- Equations of motion -- Global symmetries -- Space-time transformations -- Examples -- 1.2 Classical field equations -- Scalar field theory and spontaneous breaking of global symmetries -- Spinor fields -- 1.3 Gauge field theories -- U(1) gauge symmetry -- Non-abelian gauge symmetry -- 1.4 From classical to quantum fields (canonical quantization) -- Scalar fields -- The Feynman propagator -- Spinor fields -- Symmetry transformations for quantum fields -- 1.5 Discrete symmetries -- Space reflection -- Time reversal -- Charge conjugation -- Summary and the CPT transformation -- CP violation in the neutral… -- Problems -- 2 Path integral formulation of quantum field theory -- 2.1 Path integrals in quantum mechanics -- Transition matrix elements as path integrals -- Matrix elements of position operators -- 2.2 Vacuum-to-vacuum transitions and the imaginary time formalism -- General discussion -- Harmonic oscillator -- Euclidean Green's functions -- 2.3 Path integral formulation of quantum field theory -- Green's functions as path integrals -- Action quadratic in fields -- Gaussian integration -- 2.4 Introduction to perturbation theory -- Perturbation theory and the generating functional -- Wick's theorem -- An example: four-point Green's function in LambdaPhi -- Momentum space -- 2.5 Path integrals for fermions -- Grassmann algebra -- Anticommuting c-numbers -- Dirac propagator.

2.6 Generating functionals for Green's functions and proper vertices -- effective potential -- Classification of Green's functions and generating functionals -- Effective action -- Spontaneous symmetry breaking and effective action -- Effective potential -- 2.7 Green's functions and the scattering operator -- Problems -- 3 Feynman rules for Yang-Mills theories -- 3.1 The Faddeev-Popov determinant -- Gauge invariance and the path integral -- Faddeev-Popov determinant -- Examples -- Non-covariant gauges -- 3.2 Feynman rules for QCD -- Calculation of the Faddeev-Popov determinant -- Feynman rules -- 3.3 Unitarity, ghosts, Becchi-Rouet-Stora transformation -- Unitarity and ghosts -- BRS and anti-BRS symmetry -- Problems -- 4 Introduction to the theory of renormalization -- 4.1 Physical sense of renormalization and its arbitrariness -- Bare and 'physical' quantities -- Counterterms and the renormalization conditions -- Arbitrariness of renormalization -- Final remarks -- 4.2 Classification of the divergent diagrams -- Structure of the UV divergences by momentum power counting -- Classification of divergent diagrams -- Necessary counterterms -- 4.3 LambdaPhi: low order renormalization -- Feynman rules including counterterms -- Calculation of Fig. 4.8(b) -- Comments on analytic continuation to… -- Lowest order renormalization -- 4.4 Effective field theories -- Problems -- 5 Quantum electrodynamics -- 5.1 Ward-Takahashi identities -- General derivation by the functional technique -- Examples -- 5.2 Lowest order QED radiative corrections by the dimensional regularization technique -- General introduction -- Vacuum polarization -- Electron self-energy correction -- Electron self-energy: IR singularities regularized by photon mass -- On-shell vertex correction -- 5.3 Massless QED -- 5.4 Dispersion calculation of O(Alpha) virtual corrections in massless QED….

Self-energy calculation -- Vertex calculation -- 5.5 Coulomb scattering and the IR problem -- Corrections of order Alpha -- IR problem to all orders in Alpha -- Problems -- 6 Renormalization group -- 6.1 Renormalization group equation (RGE) -- Derivation of the RGE -- Solving the RGE -- Green's functions for rescaled momenta -- RGE in QED -- 6.2 Calculation of the renormalization group functions Beta, Gamma, Gamma -- 6.3 Fixed points -- effective coupling constant -- Fixed points -- Effective coupling constant -- 6.4 Renormalization scheme and gauge dependence of the RGE parameters -- Renormalization scheme dependence -- Effective Alpha in QED -- Gauge dependence of the Beta-function -- Problems -- 7 Scale invariance and operator product expansion -- 7.1 Scale invariance -- Scale transformations -- Dilatation current -- Conformal transformations -- 7.2 Broken scale invariance -- General discussion -- Anomalous breaking of scale invariance -- 7.3 Dimensional transmutation -- 7.4 Operator product expansion (OPE) -- Short distance expansion -- Light-cone expansion -- 7.5 The relevance of the light-cone -- Electron-positron annihilation -- Deep inelastic hadron leptoproduction -- Wilson coefficients and moments of the structure function -- 7.6 Renormalization group and OPE -- Renormalization of local composite operators -- RGE for Wilson coefficients -- OPE beyond perturbation theory -- 7.7 OPE and effective field theories -- Problems -- 8 Quantum chromodynamics -- 8.1 General introduction -- Renormalization and BRS invariance -- counterterms -- Asymptotic freedom of QCD -- The Slavnov-Taylor identities -- 8.2 The background field method -- 8.3 The structure of the vacuum in non-abelian gauge theories -- Homotopy classes and topological vacua -- Physical vacuum -- Theta-vacuum and the functional integral formalism.

8.4 Perturbative QCD and hard collisions -- Parton picture -- Factorization theorem -- 8.5 Deep inelastic electron-nucleon scattering in first order QCD (Feynman gauge) -- Structure functions and Born approximation -- Deep inelastic quark structure functions in the first order in the strong coupling constant -- Final result for the quark structure functions -- Hadron structure functions -- probabilistic interpretation -- 8.6 Light-cone variables, light-like gauge -- 8.7 Beyond the one-loop approximation -- Comments on the IR problem in QCD -- Problems -- 9 Chiral symmetry -- spontaneous symmetry breaking -- 9.1 Chiral symmetry of the QCD lagrangian -- 9.2 Hypothesis of spontaneous chiral symmetry breaking in strong interactions -- 9.3 Phenomenological chirally symmetric model of the strong interactions (Sigma-model) -- 9.4 Goldstone bosons as eigenvectors of the mass matrix and poles of Green's functions in theories with elementary scalars -- Goldstone bosons as eigenvectors of the mass matrix -- General proof of Goldstone's theorem -- 9.5 Patterns of spontaneous symmetry breaking -- 9.6 Goldstone bosons in QCD -- 10 Spontaneous and explicit global symmetry breaking -- 10.1 Internal symmetries and Ward identities -- Preliminaries -- Ward identities from the path integral -- Comparison with the operator language -- Ward identities and short-distance singularities of the operator products -- Renormalization of currents -- 10.2 Quark masses and chiral perturbation theory -- Simple approach -- Approach based on use of the Ward identity -- 10.3 Dashen's theorems -- Formulation of Dashen's theorems -- Dashen's conditions and global symmetry broken by weak gauge interactions -- 10.4 Electromagnetic… -- Electromagnetic… -- Spectral function sum rules -- Results -- 11 Higgs mechanism in gauge theories -- 11.1 Higgs mechanism.

11.2 Spontaneous gauge symmetry breaking by radiative corrections -- 11.3 Dynamical breaking of gauge symmetries and vacuum alignment -- Dynamical breaking of gauge symmetry -- Examples -- Problems -- 12 Standard electroweak theory -- 12.1 The lagrangian -- 12.2 Electroweak currents and physical gauge boson fields -- 12.3 Fermion masses and mixing -- 12.4 Phenomenology of the tree level lagrangian -- Effective four-fermion interactions -- Z couplings -- 12.5 Beyond tree level -- Renormalization and counterterms -- Corrections to gauge boson propagators -- Fermion self-energies -- Running Alpha(µ) in the electroweak theory -- Muon decay in the one-loop approximation -- Corrections to the Z partial decay widths -- 12.6 Effective low energy theory for electroweak processes -- QED as the effective low energy theory -- 12.7 Flavour changing neutral-current processes -- QCD corrections to CP violation in the neutral kaon system -- Problems -- 13 Chiral anomalies -- 13.1 Triangle diagram and different renormalization conditions -- Introduction -- Calculation of the triangle amplitude -- Different renormalization constraints for the triangle amplitude -- Important comments -- 13.2 Some physical consequences of the chiral anomalies -- Chiral invariance in spinor electrodynamics -- Pi… -- Chiral anomaly for the axial U(1) current in QCD… -- Anomaly cancellation in the SU(2) × U(1) electroweak theory -- Anomaly-free models -- 13.3 Anomalies and the path integral -- Introduction -- Abelian anomaly -- Non-abelian anomaly and gauge invariance -- Consistent and covariant anomaly -- 13.4 Anomalies from the path integral in Euclidean space -- Introduction -- Abelian anomaly with Dirac fermions -- Non-abelian anomaly and chiral fermions -- Problems -- 14 Effective lagrangians -- 14.1 Non-linear realization of the symmetry group -- Non-linear Sigma-model.

Effective lagrangian in the….

An expanded and up-dated book examining gauge theories and their symmetries.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.