Advanced Particle Physics Volume I

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 I-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 I-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 eae'e+-pair annihilation into two I-quanta. eae'e+-pair production under annihilation of two I-quanta Positronium life time Moller scattering eae' + e- a ' eae' + eae' Processes e+ + eae' a ' l + l (l = eae', I ae', I ae') 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.