Quantum Field Theory: Course Outline (PH-702)

• 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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