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

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
e⁻e⁺-pair annihilation into two γ-quanta. e⁻e⁺-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.