Lectures on Quantum Field Theory. Ashok Das

equation

       1.3.1Klein paradox

       1.4Dirac equation

       1.5References

       2Solutions of the Dirac equation

       2.1Plane wave solutions

       2.2Normalization of the wave function

       2.3Spin of the Dirac particle

       2.4Continuity equation

       2.5Dirac’s hole theory

       2.6Properties of the Dirac matrices

       2.6.1Fierz rearrangement

       2.7References

       3Properties of the Dirac equation

       3.1Lorentz transformations

       3.2Covariance of the Dirac equation

       3.3Transformation of bilinears

       3.4Projection operators, completeness relation

       3.5Helicity

       3.6Massless Dirac particle

       3.7Chirality

       3.8Non-relativistic limit of the Dirac equation

       3.9Electron in an external magnetic field

       3.10Foldy-Wouthuysen transformation

       3.11Zitterbewegung

       3.12References

       4Representations of Lorentz and Poincaré groups

       4.1Symmetry algebras

       4.1.1Rotation

       4.1.2Translation

       4.1.3Lorentz transformation

       4.1.4Poincaré transformation

       4.2Representations of the Lorentz group

       4.2.1Similarity transformations and representations

       4.3Unitary representations of the Poincaré group

       4.3.1Massive representation

       4.3.2Massless representation

       4.4References

       5Free Klein-Gordon field theory

       5.1Introduction

       5.2Lagrangian density

       5.3Quantization

       5.4Field decomposition

       5.5Creation and annihilation operators

       5.6Energy eigenstates

       5.7Physical meaning of energy eigenstates

       5.8Green’s functions

       5.9Covariant commutation relations

       5.10References

       6Self-interacting scalar field theory

       6.1Nöther’s theorem

       6.1.1Space-time translation

       6.2Self-interacting ϕ⁴ theory

       6.3Interaction picture and time evolution operator

       6.4S-matrix

       6.5Normal ordered product and Wick’s theorem

       6.6Time ordered products and Wick’s theorem

       6.7Spectral representation and dispersion relation

       6.8References

       7Complex scalar field theory

       7.1Quantization

       7.2Field decomposition

       7.3Charge operator

       7.4Green’s functions