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Indian Institute of Science Education and Research Bhopal

Physics

PHY 615: Quantum Field Theory-I (4)

Prerequisite:  PHY 305: Classical Mechanics,
                       PHY 302: Mathematical Method-II,
                       PHY 304: Quantum Mechanics-II,
                                       Special Theory of Relativity

Learning Objectives:

The course aims at introducing basic concepts of relativistic quantum theory knows as quantum field theory. Course fill focus on quantization of scalar and spinor fields and calculation of cross-sections using Feynman diagram techniques.

Course Contents:

Classical Field Theory: Introduction; Lagrangian Field Theory; Lorentz Invariance; Noether's Theorem and Conserved Currents; Hamiltonian Field Theory.

Canonical Quantization:  The Klein-Gordon Equation, The Simple Harmonic Oscillator, Free Quantum Fields, Vacuum Energy, Particles, Relativistic Normalization, Complex Scalar Fields, The Heisenberg Picture, Causality and Propagators, Applications, Non-Relativistic Field Theory

Interacting Fields: Types of Interaction, The Interaction Picture, Dyson's Formula, Scattering, Wick's Theorem, Feynman Diagrams, Feynman Rules, Amplitudes, Decays and Cross Sections, Green's Functions, Connected Diagrams and Vacuum Bubbles, Reduction Formula

The Dirac Equation:  The Lorentz Group, Clifford Algebras, The Spinor Representation, The Dirac Lagrangian, Chiral Spinors, The Weyl Equation, Parity, Majorana Spinors, Symmetries and Currents, Plane Wave Solutions.

Quantizing the Dirac Field:  Spin-Statistics Theorem, Fermionic Quantization, Fermi-Dirac Statistics, Propagators, Particles and Anti-Particles, Dirac's Hole Interpretation, Feynman Rules.

Quantum Electrodynamics:  Gauge field, Gauge Invariance, Quantization, Inclusion of Matter - QED, Lorentz Invariant Propagators; Feynman Rules; QED Processes.

Suggested Books:

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