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Explore the fundamental principles of quantum field theory through this comprehensive lecture series covering scalar field quantization, relativistic causality, and the Dirac equation derivation from group theory. Master plane wave solutions to the Dirac equation and fermion quantization techniques while delving into Maxwell Lagrangian derivation and electromagnetic field quantization using both Coulomb gauge and Gupta-Bleuler methods. Learn the interaction picture, S-matrix formalism, and LSZ reduction for scalar bosons, then advance to Wick's theorem and calculations of decay rates and scattering cross sections. Discover how to derive the QED Lagrangian and Feynman rules, then apply these concepts to analyze Compton scattering with Klein-Nishina formula derivation, pair annihilation processes, and Moller and Bhabha differential scattering cross sections. Study muon-antimuon pair production, Bethe-Heitler formula for bremsstrahlung, and pair creation in nuclear electric fields before examining one-loop quantum corrections including the anomalous magnetic moment of the electron. Progress through scalar QED applications including Compton scattering, pair annihilation, Moller scattering, bremsstrahlung, and pair creation processes. Advance to Yang-Mills theory and quantum chromodynamics (QCD) derivation, then explore spontaneous symmetry breaking and the Higgs mechanism through SO(3) and SU(3) examples. Understand fermion mass generation via Yukawa interactions and construct the complete quantum electroweak theory Lagrangian leading to the Standard Model of particle physics. Learn methods for incorporating neutrino masses and coupling spinors to gravity through curved Dirac equation derivation. Conclude with advanced topics including coupling QED and QCD to gravity, Bhabha scattering using spinor helicity formalism, and covariant bosonic string quantization using the Dirac method.
