Quantum field theory.

This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive ap...

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Bibliographic Details
Main Author: Sadovskiĭ, M. V. 1948- (Author)
Format: eBook
Language:English
Published: Berlin : De Gruyter, 2013.
Series:De Gruyter studies in mathematical physics ; 17.
Subjects:
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Table of Contents:
  • Preface; 1 Basics of elementary particles; 1.1 Fundamental particles; 1.1.1 Fermions; 1.1.2 Vector bosons; 1.2 Fundamental interactions; 1.3 The Standard Model and perspectives; 2 Lagrange formalism. Symmetries and gauge fields; 2.1 Lagrange mechanics of a particle; 2.2 Real scalar field. Lagrange equations; 2.3 The Noether theorem; 2.4 Complex scalar and electromagnetic fields; 2.5 Yang-Mills fields; 2.6 The geometry of gauge fields; 2.7 A realistic example
  • chromodynamics; 3 Canonical quantization, symmetries in quantum field theory; 3.1 Photons.
  • 3.1.1 Quantization of the electromagnetic field3.1.2 Remarks on gauge invariance and Bose statistics; 3.1.3 Vacuum fluctuations and Casimir effect; 3.2 Bosons; 3.2.1 Scalar particles; 3.2.2 Truly neutral particles; 3.2.3 CPT-transformations; 3.2.4 Vector bosons; 3.3 Fermions; 3.3.1 Three-dimensional spinors; 3.3.2 Spinors of the Lorentz group; 3.3.3 The Dirac equation; 3.3.4 The algebra of Dirac's matrices; 3.3.5 Plane waves; 3.3.6 Spin and statistics; 3.3.7 C, P, T transformations for fermions; 3.3.8 Bilinear forms; 3.3.9 The neutrino.
  • 4 The Feynman theory of positron and elementary quantum electrodynamics4.1 Nonrelativistic theory. Green's functions; 4.2 Relativistic theory; 4.3 Momentum representation; 4.4 The electron in an external electromagnetic field; 4.5 The two-particle problem; 5 Scattering matrix; 5.1 Scattering amplitude; 5.2 Kinematic invariants; 5.3 Unitarity; 6 Invariant perturbation theory; 6.1 Schroedinger and Heisenberg representations; 6.2 Interaction representation; 6.3 S-matrix expansion; 6.4 Feynman diagrams for electron scattering in quantum electrodynamics; 6.5 Feynman diagrams for photon scattering.
  • 6.6 Electron propagator6.7 The photon propagator; 6.8 The Wick theorem and general diagram rules; 7 Exact propagators and vertices; 7.1 Field operators in the Heisenberg representation and interaction representation; 7.2 The exact propagator of photons; 7.3 The exact propagator of electrons; 7.4 Vertex parts; 7.5 Dyson equations; 7.6 Ward identity; 8 Some applications of quantum electrodynamics; 8.1 Electron scattering by static charge: higher order corrections; 8.2 The Lamb shift and the anomalous magnetic moment; 8.3 Renormalization
  • how it works; 8.4 "Running" the coupling constant.
  • 8.5 Annihilation of e+ẽ into hadrons. Proof of the existence of quarks8.6 The physical conditions for renormalization; 8.7 The classification and elimination of divergences; 8.8 The asymptotic behavior of a photon propagator at large momenta .; 8.9 Relation between the "bare" and "true" charges; 8.10 The renormalization group in QED; 8.11 The asymptotic nature of a perturbation series; 9 Path integrals and quantum mechanics; 9.1 Quantum mechanics and path integrals; 9.2 Perturbation theory; 9.3 Functional derivatives; 9.4 Some properties of functional integrals.