Lectures on Quantum Field Theory. Ashok Das

7.5Spontaneous symmetry breaking and the Goldstone theorem

       7.6Electromagnetic coupling

       7.7References

       8Dirac field theory

       8.1Pauli exclusion principle

       8.2Quantization of the Dirac field

       8.3Field decomposition

       8.4Charge operator

       8.5Green’s functions

       8.6Covariant anti-commutation relations

       8.7Normal ordered and time ordered products

       8.8Massless Dirac fields

       8.9Yukawa interaction

       8.10Feynman diagrams

       8.11References

       9Maxwell field theory

       9.1Maxwell’s equations

       9.2Canonical quantization

       9.3Field decomposition

       9.4Photon propagator

       9.5Quantum electrodynamics

       9.6Physical processes

       9.7Ward-Takahashi identity in QED

       9.8Covariant quantization of the Maxwell theory

       9.9References

       10Dirac method for constrained systems

       10.1Constrained systems

       10.2Dirac method and Dirac bracket

       10.3Particle moving on a sphere

       10.4Relativistic free particle

       10.5Dirac field theory

       10.6Maxwell field theory

       10.7References

       11Discrete symmetries

       11.1Parity

       11.1.1Parity in quantum mechanics

       11.1.2Spin zero field

       11.1.3Photon field

       11.1.4Dirac field

       11.2Charge conjugation

       11.2.1Spin zero field

       11.2.2Dirac field

       11.2.3Majorana fermions

       11.2.4Eigenstates of charge conjugation

       11.3Time reversal

       11.3.1Spin zero field and Maxwell’s theory

       11.3.2Dirac fields

       11.3.3 Consequences of T invariance

       11.3.4Electric dipole moment of neutron

       11.4CPT theorem

       11.4.1Equality of mass for particles and antiparticles

       11.4.2Electric charge for particles and antiparticles

       11.4.3Equality of lifetimes for particles and antiparticles

       11.5References

       12Yang-Mills theory

       12.1Non-Abelian gauge theories

       12.2Canonical quantization of Yang-Mills theory

       12.3Path integral quantization of gauge theories

       12.4Path integral quantization of tensor fields

       12.5References

       13BRST invariance and its consequences

       13.1BRST symmetry

       13.2Covariant quantization of Yang-Mills theory

       13.3Unitarity

       13.4Slavnov-Taylor identity

       13.5Feynman rules

       13.6Ghost free gauges

       13.7References

       14Higgs phenomenon and the standard model

       14.1Stückelberg formalism

       14.2Higgs phenomenon

       14.3The standard model

       14.3.1Field content

       14.3.2Lagrangian density

       14.3.3Spontaneous symmetry breaking

       14.4References

       15Regularization of Feynman diagrams

       15.1Introduction

       15.2Loop expansion

       15.3Cut-off regularization

       15.3.1Calculation in the Yukawa theory

       15.4Pauli-Villars regularization

       15.5Dimensional regularization

       15.5.1Calculations in QED

       15.6References

       16Renormalization theory

       16.1Superficial degree of divergence

       16.2A brief history of renormalization

       16.3Schwinger-Dyson equation

       16.4BPHZ renormalization

       16.5Renormalization of gauge theories

       16.6Anomalous Ward identity

       16.7References

       17Renormalization group and equation

       17.1Gell-Mann-Low equation

       17.2Renormalization group

       17.3Renormalization group equation