Quantum Field Theory 2nd Edition by Michael Sadovskii 3110645157 9783110645156

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ISBN 10: 3110645157

ISBN 13: 9783110645156

Author: Michael V. Sadovskii

 This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The theoretical results are derived using the physical phenomena as a starting point. This inductive approach allows a deep understanding of the methods used for solving problems in this field. This second, revised edition is expanded with biographical notes contextualizing the main results in quantum field theory.

Quantum Field Theory 2nd Table of contents:

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 field

3.1.2 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 electrodynamics

4.1 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 propagator

6.7 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+e− into hadrons. Proof of the existence of quarks

8.6 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

10 Functional integrals: scalars and spinors

10.1 The generating functional for scalar fields

10.2 Functional integration

10.3 Free-particle Green’s functions

10.4 The Generating functional for interacting fields

10.5 φ4 theory

10.6 The generating functional for connected diagrams

10.7 Self-energy and vertex functions

10.8 The theory of critical phenomena

10.9 Functional methods for fermions

10.10 Propagators and gauge conditions in QED

11 Functional integrals: gauge fields

11.1 Non-Abelian gauge fields and Faddeev–Popov quantization

11.2 Feynman diagrams for non-Abelian theory

12 The Weinberg–Salam model

12.1 Spontaneous symmetry-breaking and the Goldstone theorem

12.2 Gauge fields and the Higgs phenomenon

12.3 Yang–Mills fields and spontaneous symmetry-breaking

12.4 The Weinberg–Salam model

13 Renormalization

13.1 Divergences in φ4

13.2 Dimensional regularization of φ4 -theory

13.3 Renormalization of φ4 -theory

13.4 The renormalization group

13.5 Asymptotic freedom of the Yang–Mills theory

13.6 “Running” coupling constants and the “grand unification”

14 Nonperturbative approaches

14.1 The lattice field theory

14.2 Effective potential and loop expansion

14.3 Instantons in quantum mechanics

14.4 Instantons and the unstable vacuum in field theory

14.5 The Lipatov asymptotics of a perturbation series

14.6 The end of the “zero-charge” story?

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