Syllabus
Unit 1
Non-relativistic quantum field theory: quantum mechanics of many particle systems; second quantisation; Schrodinger equation as a classical field equation and its quantisation; inclusion of inter-particle interactions in the first and second quantised formalism
Unit 2
Canonical quantization of free fields: Real and complex scalar fields, Dirac field, electromagnetic field, Bilinear covariants, Projection operators, Charge conjugation and Parity on scalar, Dirac and electromagnetic fields.
Unit 3
Interacting fields: Interaction picture, Interacting Klein-Gordon field, Covariant perturbation theory, S-matrix and its computation from n-point Green functions, Wick’s theorem, Feynman diagrams.
Unit 4
QED: Feynman rules, Example of actual calculations: Rutherford, Bhabha, Moeller, Compton etc. Decay and scattering kinematics. Mandelstam variables and use of crossing symmetry, coupling Dirac field to electromagnetic field, Feynman rules for computing Green functions, symmetries and Ward identity.
Unit 5
Higher order corrections: One-loop diagrams. Basic idea of regularization and renormalization, Landau pole. Degree of divergence, Calculation of self-energy of scalar in φ4 theory using cut-off or dimensional regularization, Path integrals for scalar and fermionic fields.
Gauge theories: Gauge invariance in QED, non-abelian gauge theories (classical theory, quantization), QCD (introduction), Asymptotic freedom, Spontaneous symmetry breaking, Goldstone theorem, Higgs mechnism,Yang-Mills theory.
Objectives
Course Objectives: To learn the basic concepts and techniques of quantum field theory, with applications to elementary particle physics, with special emphasis to Quantum Electrodynamics (QED).