**[Cr:4, Lc:3, Tt:1, Lb:0]**

Knowledge of the content of **PHY302**, **PHY303** and **PHY306** is essential to follow this course.

Goal: To trace the path from single particle Non-relativistic Quantum Mechanics (QM) to the necessity of many body interpretations of its relativistic generalizations. Introduction of Quantum field theory as a comprehensive language to describe many body relativistic quantum systems which resolves the paradoxes of single body Relativistic QM.

- Relativistic Quantum Mechanics: Klein-Gordon equation, Dirac equation and its plane wave solutions, significance of negative energy solutions, spin angular momentum of the Dirac particle. Non-relativistic limit of Dirac equation, Electron in electromagnetic fields, spin magnetic moment, spin-orbit interaction. Problems of relativistic one-particle theories and the need for QFT.
- Classical field Theory: Symmetries and Noether's theorem. Stress-energy tensor and propagator theory for Schrodinger, Klein-Gordon and Dirac theories.
- Relativistic Quantum Field Theory: Canonical quantization of real and complex scalar fields. Quantization of Spin half-field. Dirac, Weyl and Majorana fields. Wick's theorem for spin 0, 1/2. Heisenberg and Interaction pictures and Perturbation theory for correlation functions. Feynman rules for correlators. Spin-statistics theorem (non-interacting), Causality.

- J. J. Sakurai, Advanced Quantum Mechanics, (Pearson), 1967.
- A. Lahiri and P. Pal, A First Book of Quantum Field Theory, (Narosa), 2007.
- M. Peskin and D. Schroeder, An introduction to Quantum Field Theory, (Westview Press), 1995.
- H. Mandl and G. Shaw, Quantum Field Theory, (Wiley-Blackwell), 2010.
- M. Srednicki, Quantum Field Theory, (Cambridge University Press), 2007.
- L. H. Ryder, Quantum Field Theory, (Cambridge University Press), 1996.