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Quantum Field Theory: Course Outline (PH-702)

A field theory that incorporates quantum mechanics and the principles of the theory of relativity.

Course Outline

  • Preliminaries.
  • Classical Lagrangian Dynamics.
  • Lagrangian Field Theory.
  • Global and Local Symmetries.
  • Noether's Theorem.
  • Canonical Quantization.
  • From Classical to Quantum Mechanics.
  • Quantum Fields and Causality.
  • Canonical Quantization of Scalar Field Theory.
  • Complex Fields and Anti-Particles.
  • The S-Matrix in Quantum Field Theory.
  • Time Evolution of Quantum States and the S-Matrix.
  • Feynman Propagator and Wick's Theorem.
  • Transition Amplitudes and Feynman Rules.
  • Particle Decays and Cross Sections.
  • Unitarity and the Optical Theorem.
  • Quantum Electrodynamics.
  • Weyl and Dirac Spinors.
  • Quantization of the Fermion Field.
  • Gauge Symmetry.
  • Quantization of the Electromagnetic Field.
  • The Photon Propagator and Gauge Fixing.
  • Becchi-Rouet-Stora Transformations.
  • Feynman Rules for Quantum Electrodynamics.
  • Renormalization.
  • Renormalizability.
  • Dimensional Regularization.
  • Renormalization of a Scalar Theory.
  • Displacement Operator Formalism of Renormalization to All Orders.
  • Renormalization Group Equation.
  • Anomalous magnetic moment and the Lamb shift.

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