Syllabus

Module 1: (7 hours)
Brief introduction to relativistic quantum mechanics and its shortcomings. Classical field theory, Lorentz invariance, symmetries and Noether’s theorem.

Module 2: (8 hours)
Quantum field theory, canonical quantization of fields, free real scalar field, complex scalar field theory, interpretation of particles in field theory, causality, Green’s function, and Feynman propagator of the scalar field.

Module 3: (7 hours)
The interacting quantum field theory, ?f4 theory, Dyson’s formula, Wick’s theorem, Feynman rules and diagram for ?f4 theory, connected and disconnected diagrams, Feynman propagator and S-Matrices.

Module 4: (10 hours)
Spinor representation, Gamma-Matrices, Dirac action and Lagrangian, Dirac equation, Symmetries and Conserved Currents, quantising the Dirac field, spin ½ particles, Feynman propagator for Dirac field.

Module 5: (6 hours)
A brief introduction to quantum electrodynamics: Maxwell equations, gauge symmetry, quantization of the electromagnetic fields.

To understand the algebra of the Lorentz group and its representations on different fields.

To learn the quantization of various fields, leading to particles with different spins.

Formulation of elementary particle interaction in terms of fields.

To introduce the basic idea of propagators, interaction, and Feynman diagrams.

5. To introduce the basic idea of S-matrix and decay widths.

At the end of the course, students will be able to:
CO1: Describe the reasons for the failure of relativistic quantum mechanics and the need for quantum field theory.

CO2: Understand the algebra of the Lorentz group and its representations on different fields.

CO3: Understand the canonical quantization of fields with emphasis on scalar and fermionic fields.

CO4: Understand the mathematical description of the physical processes of particle creation, destruction, and interactions.

CO5: Calculate cross-sections and decay widths using the Feynman rules and learn the rudiments of mathematical formalism developed to study particle physics.

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Boulder, CO: Westview Press, Levant (2005).

L. H. Ryder, Quantum Field Theory, Cambridge University press , 2nd Edition (1998).

D. Tong, Quantum field theory, Lecture notes.

S. Coleman, Lectures of quantum field theory, World Scientific.