Gauge theories in particle physics a practical introduction. Volume 1, From relativistic quantum mechanics to QED

Gauge theories in particle physics a practical introduction Volume 1, From relativistic quantum mechanics to QED Volume 1, From relativistic quantum mechanics to QED /

The fourth edition of this well-established, highly regarded two-volume set continues to provide a fundamental introduction to advanced particle physics while incorporating substantial new experimental results, especially in the areas of CP violation and neutrino oscillations. It offers an accessibl...

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Detalles Bibliográficos
Otros Autores: Aitchison, Ian J. R., author (author), Hey, Anthony J. G., author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Boca Raton, Florida ; London, England ; New York : CRC Press [2013]
Edición:4th ed
Materias:
Gauge fields (Physics)
Particles (Nuclear physics)
Weak interactions (Nuclear physics)
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009624646506719
Tabla de Contenidos:
  • Cover
  • Volume 1
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Dedication Page
  • Contents
  • Preface
  • I Introductory Survey, Electromagnetism as a Gauge Theory, and Relativistic Quantum Mechanics
  • 1 The Particles and Forces of the Standard Model
  • 1.1 Introduction: the Standard Model
  • 1.2 The fermions of the Standard Model
  • 1.2.1 Leptons
  • 1.2.2 Quarks
  • 1.3 Particle interactions in the Standard Model
  • 1.3.1 Classical and quantum fields
  • 1.3.2 The Yukawa theory of force as virtual quantum exchange
  • 1.3.3 The one-quantum exchange amplitude
  • 1.3.4 Electromagnetic interactions
  • 1.3.5 Weak interactions
  • 1.3.6 Strong interactions
  • 1.3.7 The gauge bosons of the Standard Model
  • 1.4 Renormalization and the Higgs sector of the Standard Model
  • 1.4.1 Renormalization
  • 1.4.2 The Higgs boson of the Standard Model
  • 1.5 Summary
  • Problems
  • 2 Electromagnetism as a Gauge Theory
  • 2.1 Introduction
  • 2.2 The Maxwell equations: current conservation
  • 2.3 The Maxwell equations: Lorentz covariance and gauge invariance
  • 2.4 Gauge invariance (and covariance) in quantum mechanics
  • 2.5 The argument reversed: the gauge principle
  • 2.6 Comments on the gauge principle in electromagnetism
  • Problems
  • 3 Relativistic Quantum Mechanics
  • 3.1 The Klein-Gordon equation
  • 3.1.1 Solutions in coordinate space
  • 3.1.2 Probability current for the KG equation
  • 3.2 The Dirac equation
  • 3.2.1 Free-particle solutions
  • 3.2.2 Probability current for the Dirac equation
  • 3.3 Spin
  • 3.4 The negative-energy solutions
  • 3.4.1 Positive-energy spinors
  • 3.4.2 Negative-energy spinors
  • 3.4.3 Dirac's interpretation of the negative-energy solutions of the Dirac equation
  • 3.4.4 Feynman's interpretation of the negative-energy solutions of the KG and Dirac equations.
  • 3.5 Inclusion of electromagnetic interactions via the gauge principle: the Dirac prediction of g = 2 for the electron
  • Problems
  • 4 Lorentz Transformations and Discrete Symmetries
  • 4.1 Lorentz transformations
  • 4.1.1 The KG equation
  • 4.1.2 The Dirac equation
  • 4.2 Discrete transformations: P, C and T
  • 4.2.1 Parity
  • 4.2.2 Charge conjugation
  • 4.2.3 CP
  • 4.2.4 Time reversal
  • 4.2.5 CPT
  • Problems
  • II Introduction to Quantum Field Theory
  • 5 Quantum Field Theory I: The Free Scalar Field
  • 5.1 The quantum field: (i) descriptive
  • 5.2 The quantum field: (ii) Lagrange-Hamilton formulation
  • 5.2.1 The action principle: Lagrangian particle mechanics
  • 5.2.2 Quantum particle mechanics à la Heisenberg-Lagrange-Hamilton
  • 5.2.3 Interlude: the quantum oscillator
  • 5.2.4 Lagrange-Hamilton classical field mechanics
  • 5.2.5 Heisenberg-Lagrange-Hamilton quantum field mechanics
  • 5.3 Generalizations: four dimensions, relativity and mass
  • Problems
  • 6 Quantum Field Theory II: Interacting Scalar Fields
  • 6.1 Interactions in quantum field theory: qualitative introduction
  • 6.2 Perturbation theory for interacting fields: the Dyson expansion of the S-matrix
  • 6.2.1 The interaction picture
  • 6.2.2 The S-matrix and the Dyson expansion
  • 6.3 Applications to the 'ABC' theory
  • 6.3.1 The decay C A + B
  • 6.3.2 A + B A + B scattering: the amplitudes
  • 6.3.3 A + B A + B scattering: the Yukawa exchange mechanism, s and u channel processes
  • 6.3.4 A + B A + B scattering: the differential cross section
  • 6.3.5 A + B A + B scattering: loose ends
  • Problems
  • 7 Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields
  • Introduction of Electromagnetic Interactions
  • 7.1 The complex scalar field: global U(1) phase invariance, particles and antiparticles
  • 7.2 The Dirac field and the spin-statistics connection.
  • 7.3 The Maxwell field Aμ(x)
  • 7.3.1 The classical field case
  • 7.3.2 Quantizing Aμ(x)
  • 7.4 Introduction of electromagnetic interactions
  • 7.5 P, C and T in quantum field theory
  • 7.5.1 Parity
  • 7.5.2 Charge conjugation
  • 7.5.3 Time reversal
  • Problems
  • III Tree-Level Applications in QED
  • 8 Elementary Processes in Scalar and Spinor Electrodynamics
  • 8.1 Coulomb scattering of charged spin-0 particles
  • 8.1.1 Coulomb scattering of s+ (wavefunction approach)
  • 8.1.2 Coulomb scattering of s+ (field-theoretic approach)
  • 8.1.3 Coulomb scattering of s−
  • 8.2 Coulomb scattering of charged spin-½ particles
  • 8.2.1 Coulomb scattering of e− (wavefunction approach)
  • 8.2.2 Coulomb scattering of e−(field-theoretic approach)
  • 8.2.3 Trace techniques for spin summations
  • 8.2.4 Coulomb scattering of e+
  • 8.3 e−s+ scattering
  • 8.3.1 The amplitude for e−s+ e−s+
  • 8.3.2 The cross section for e−s+ e−s+
  • 8.4 Scattering from a non-point-like object: the pion form factor in e−π+ e−π+
  • 8.4.1 e− scattering from a charge distribution
  • 8.4.2 Lorentz invariance
  • 8.4.3 Current conservation
  • 8.5 The form factor in the time-like region: e+e− π+π− and crossing symmetry
  • 8.6 Electron Compton scattering
  • 8.6.1 The lowest-order amplitudes
  • 8.6.2 Gauge invariance
  • 8.6.3 The Compton cross section
  • 8.7 Electronmuon elastic scattering
  • 8.8 Electron-proton elastic scattering and nucleon form factors
  • 8.8.1 Lorentz invariance
  • 8.8.2 Current conservation
  • Problems
  • 9 Deep Inelastic Electron-Nucleon Scattering and the Parton Model
  • 9.1 Inelastic electron-proton scattering: kinematics and structure functions
  • 9.2 Bjorken scaling and the parton model
  • 9.3 Partons as quarks and gluons
  • 9.4 The Drell-Yan process
  • 9.5 e+e− annihilation into hadrons
  • Problems
  • IV Loops and Renormalization.
  • 10 Loops and Renormalization I: The ABC Theory
  • 10.1 The propagator correction in ABC theory
  • 10.1.1 The O(g2) self-energy ∏[2]C (q2)
  • 10.1.2 Mass shift
  • 10.1.3 Field strength renormalization
  • 10.2 The vertex correction
  • 10.3 Dealing with the bad news: a simple example
  • 10.3.1 Evaluating ∏[2]C (q2)
  • 10.3.2 Regularization and renormalization
  • 10.4 Bare and renormalized perturbation theory
  • 10.4.1 Reorganizing perturbation theory
  • 10.4.2 The O(g2ph) renormalized self-energy revisited: how counter terms are determined by renormalization conditions
  • 10.5 Renormalizability
  • Problems
  • 11 Loops and Renormalization II: QED
  • 11.1 Counter terms
  • 11.2 The O(e2) fermion self-energy
  • 11.3 The O(e2) photon self-energy
  • 11.4 The O(e2) renormalized photon self-energy
  • 11.5 The physics of ∏̅γ[2] (q2)
  • 11.5.1 Modified Coulomb's law
  • 11.5.2 Radiatively induced charge form factor
  • 11.5.3 The running coupling constant
  • 11.5.4 ∏̅γ[2] in the s-channel
  • 11.6 The O(e2) vertex correction, and Z1 = Z2
  • 11.7 The anomalous magnetic moment and tests of QED
  • 11.8 Which theories are renormalizable - and does it matter?
  • Problems
  • A Non-relativistic Quantum Mechanics
  • B Natural Units
  • C Maxwell's Equations: Choice of Units
  • D Special Relativity: Invariance and Covariance
  • E Dirac δ-Function
  • F Contour Integration
  • G Green Functions
  • H Elements of Non-relativistic Scattering Theory
  • H.1 Time-independent formulation and differential cross section
  • H.2 Expression for the scattering amplitude: Born approximation
  • H.3 Time-dependent approach
  • I The Schrödinger and Heisenberg Pictures
  • J Dirac Algebra and Trace Identities
  • J.1 Dirac algebra
  • J.1.1 γ matrices
  • J.1.2 γ5 identities
  • J.1.3 Hermitian conjugate of spinor matrix elements
  • J.1.4 Spin sums and projection operators
  • J.2 Trace theorems.
  • K Example of a Cross Section Calculation
  • K.1 The spin-averaged squared matrix element
  • K.2 Evaluation of two-body Lorentz-invariant phase space in 'laboratory' variables
  • L Feynman Rules for Tree Graphs in QED
  • L.1 External particles
  • L.2 Propagators
  • L.3 Vertices
  • References
  • Index
  • Volume 2
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Dedication Page
  • Contents
  • Preface
  • V Non-Abelian Symmetries
  • 12 Global Non-Abelian Symmetries
  • 12.1 The Standard Model
  • 12.2 The flavour symmetry SU(2)f
  • 12.2.1 The nucleon isospin doublet and the group SU(2)
  • 12.2.2 Larger (higher-dimensional) multiplets of SU(2) in nuclear physics
  • 12.2.3 Isospin in particle physics: flavour SU(2)f
  • 12.3 Flavour SU(3)f
  • 12.4 Non-Abelian global symmetries in Lagrangian quantum field theory
  • 12.4.1 SU(2)f and SU(3)f
  • 12.4.2 Chiral symmetry
  • Problems
  • 13 Local Non-Abelian (Gauge) Symmetries
  • 13.1 Local SU(2) symmetry
  • 13.1.1 The covariant derivative and interactions with matter
  • 13.1.2 The non-Abelian field strength tensor
  • 13.2 Local SU(3) Symmetry
  • 13.3 Local non-Abelian symmetries in Lagrangian quantum field theory
  • 13.3.1 Local SU(2) and SU(3) Lagrangians
  • 13.3.2 Gauge field self-interactions
  • 13.3.3 Quantizing non-Abelian gauge fields
  • Problems
  • VI QCD and the Renormalization Group
  • 14 QCD I: Introduction, Tree Graph Predictions, and Jets
  • 14.1 The colour degree of freedom
  • 14.2 The dynamics of colour
  • 14.2.1 Colour as an SU(3) group
  • 14.2.2 Global SU(3)c invariance, and 'scalar gluons'
  • 14.2.3 Local SU(3)c invariance: the QCD Lagrangian
  • 14.2.4 The θ-term
  • 14.3 Hard scattering processes, QCD tree graphs, and jets
  • 14.3.1 Introduction
  • 14.3.2 Two-jet events in p̅p collisions
  • 14.3.3 Three-jet events in p̅p collisions
  • 14.4 3-jet events in e+e− annihilation.
  • 14.4.1 Calculation of the parton-level cross section.

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