Advanced Particle Physics Volume I : Particles, Fields, and Quantum Electrodynamics book cover
1st Edition

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

ISBN 9781138115996
Published May 24, 2017 by CRC Press
655 Pages 117 B/W Illustrations

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Book Description

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.

Table of Contents

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
CPT theorem

Fundamental Interactions

Species of interactions
On path to unified field theory

Atoms — Nuclei — Nucleons
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
Neutrino telescopes

Scalar Field

Klein–Gordon equation
Production and destruction operators
Wave-corpuscle dualism
Commutation relations. Properties of commutator functions
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


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

Scattering of Electrons and Positrons
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


Problems and References appear at the end of each section.

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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.