1st Edition

Advanced Particle Physics Volume I Particles, Fields, and Quantum Electrodynamics

By Oleg Boyarkin Copyright 2011
    655 Pages 117 B/W Illustrations
    by CRC Press

    656 Pages 117 B/W Illustrations
    by CRC Press

    Helping readers understand the complicated laws of nature, Advanced Particle Physics Volume I: Particles, Fields, and Quantum Electrodynamics explains the calculations, experimental procedures, and measuring methods of particle physics. It also describes modern physics devices, including accelerators, elementary particle detectors, and neutrino telescopes.

    The book first introduces the mathematical basis of modern quantum field theory. It presents the most pertinent information on group theory, proves Noether’s theorem, and determines the major motion integrals connected with both space and internal symmetry. The second part on fundamental interactions and their unifications discusses the main theoretical preconditions and experiments that allow for matter structure to be established at the quark-lepton level. In the third part, the author investigates the secondary quantized theories of free fields with spin 0, 1/2, and 1, with particular emphasis on the neutrino field. The final part focuses on quantum electrodynamics, the first successfully operating quantum field theory. Along with different renormalization schemes of quantum field theory, the author covers the calculation methods for polarized and unpolarized particles, with and without inclusion of radiative corrections.

    Each part in this volume contains problems to help readers master the calculation techniques and generalize the results obtained. To improve understanding of the computation procedures in quantum field theory, the majority of the calculations have been performed without dropping complex intermediate steps.

    MATHEMATICAL PRELUDE
    Relativistic Invariance

    Three-Dimensional World
    Orthogonal transformation group O(3)
    Tensor representations of the SO(3)-group

    The Four-Dimensional Minkowski Space
    The homogeneous Lorenz group
    Classification of irreducible representations of the Lorentz homogeneous group
    Tensor representations of the limited homogeneous Lorentz group
    Spinor representations of the homogeneous Lorentz group
    Poincare group and its representations

    Lagrangian Formulation of Field Theory
    Principle of least action. Lagrange–Euler equations
    Noether theorem and dynamic invariants
    Energy-momentum tensor
    Moment of momentum tensor
    Electromagnetic current vector and electric charge
    Isotopic spin

    Discrete Symmetry Operations
    Spatial inversion
    Time inversion
    Charge conjugation
    G-parity
    CPT theorem

    BIRD’S-EYE VIEW ON MICROWORLD
    Fundamental Interactions

    Species of interactions
    On path to unified field theory

    Atoms — Nuclei — Nucleons
    Atomism
    Rutherford model of atom
    Structure of atomic nucleus

    From Muon to Gluon

    Hadron Families
    Yukawa hypothesis
    Isotopic multiplets
    Unitary multiplets

    Quark "Atoms"
    Hypothesis of fundamental triplets
    X-ray photography of nucleons
    Parton model
    Quantum chromodynamics. The first acquaintance
    Heavy quarks and flavor symmetries

    Passing Glance on Theory of Electroweak Interaction
    Spontaneous symmetry breaking
    Glashow–Weinberg–Salam theory

    Fundamental Particles of Standard Model

    Technical Equipments of Particle Physics
    Accelerators
    Detectors
    Neutrino telescopes

    QUANTUM IDYLL — FREE FIELDS
    Scalar Field

    Klein–Gordon equation
    Quantization
    Production and destruction operators
    Wave-corpuscle dualism
    Commutation relations. Properties of commutator functions
    Microcausality
    Relativistically covariant scheme of canonical quantization
    Green function of scalar field
    Causal Green function
    Chronological product. Convolution of operators
    First order equation for scalar particles

    Particles with Spin 1/2
    Dirac equation
    Calculating γ-matrix tracks
    Relativistic covariance
    Solutions of free Dirac equation
    Once more about particles spin
    Polarization density matrix for Dirac particles
    Dirac equation in external electromagnetic field
    Charge conjugation, spatial inversion and time inversion for Dirac field
    Relativistic quantization scheme
    Dirac field quantization (momentum space)
    Dirac field quantization (configuration space)
    Majorana equation
    Quantization of Majorana field
    Second quantized representation of discrete operations C, P and T for particles with spin 1/2
    Neutrino in Dirac and Majorana theory

    Massive Vector Field
    Proca equation
    Dynamic invariants of vector field
    Commutation relations in Proca theory
    Duffin–Kemmer equation for vector field

    Electromagnetic Field
    Maxwell equations
    Dynamic invariants of electromagnetic field
    Electromagnetic field quantization
    Quantization with use of indefinite metric
    Photon polarization

    QUANTUM ELECTRODYNAMICS
    S-Matrix

    Equations and dynamic variables in Heisenberg representation
    Interaction representation
    Scattering matrix
    Representation of S-matrix as sum of normal products
    Calculation of S-matrix elements
    Feynman rules in coordinate space
    Furry’s theorem
    Feynman rules in momentum representation
    Crossing symmetry
    Cross section for unpolarized particles
    Cross section for scattering by external fields
    Decays of elementary particles
    Cross section for polarized particles
    Statistical hypothesis

    Transmission of γ-Radiation through Matter
    Photoeffect (nonrelativistic case)
    Photoeffect (relativistic case)
    Compton-effect (unpolarized case)
    Compton-effect (polarized case)
    Electron-positron pair production by photon in nucleus field
    Resume

    Scattering of Electrons and Positrons
    Bremsstrahlung
    Radiation of long-wave photons. Infrared catastrophe
    ee+-pair annihilation into two γ-quanta. ee+-pair production under annihilation of two γ-quanta
    Positronium life time
    Möller scattering e+ e- → e + e
    Processes e+ + e → l + l (l = e, μ, τ )

    Radiative Corrections
    Calculations of integrals over virtual momenta
    Regularization methods
    Self-energy of electron
    Vacuum polarization
    Vertex function of the third order
    Radiative corrections to scattering of electron by Coulomb nucleus field
    Anomalous magnetic moment of leptons
    Lamb shift

    Renormalization Theory
    Primitive divergent diagrams
    Effective elements of Feynman diagrams
    Ward identity
    Extraction of divergences
    QED renormalizability
    Renormalization group
    Consistency problems of the QED

    Appendix

    Problems and References appear at the end of each section.

    Biography

    Oleg Boyarkin is a professor of theoretical physics at Belarus State Pedagogical University. Dr. Boyarkin has authored several physics books and was nominated as International Scientist of the Year 2007 by the International Biographical Centre of Cambridge.