**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*:

- Peskin, Michael E., and Daniel V. Schroeder. An Introduction to Quantum Field Theory. Boulder, CO: Westview Press, 1995.

ISBN: 9780201503975. - Quantum Field Theory by Ryder
- Quantum Field Theory Part 1 by Steven Weinberg

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