Details of ID4112 (Autumn 2012)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
ID4112 Quantum Field theory Ritesh Kumar Singh

Syllabus

The transition from discrete to a continuous system, action principle the Lagrangian formulation for continuous systems, functional derivatives and the equation of motion, stress-energy tensor, the Hamiltonian formulation.





Galilean and Lorentz invariance, relativistic systems representations of the Lorentz-Poincare group. Gauge invariance. Continuous symmetries and Noether's theorem.



Attempts at relativistic quantum mechanics, the Klein-Gordon and Dirac equations, problems with single particle relativistic quantum theory.



Spin zero systems : canonical quantization of scalar fields, the spin-statistics theorem, the LSZ reduction formula. Review of path integrals in quantum mechanics. Path integral for free scalar theory, path integral for interacting field theory. Scattering amplitudes, Feynman rules, cross-section and decay rates.



The Lehmann-Kalln form of the exact propagator, loop corrections to the propagator and the vertex, higher order corrections and renormalizability. Two particle elastic scattering at one loop. The effective action.



Divergence structure, power counting, renormalization counter terms, types of regularization. Renormalization group.



Continuous symmetries, conserved currents, Ward-Takahashi identities, discrete symmetries, nonabelian symmetries.



Spin - representations of the Lorenz group, left and right handed spinors, Weyl, Dirac and Majorana representations, canonical quantization, discrete symmetries for fermions, fermionic path integrals.



Spin-1 representations, Maxwell's equations, Gupta-Bleuler quantization of the Maxwell field.



Quantum electrodynamics, Feynman rules, gamma matrix technology, calculation of spin averaged cross-sections, renormalization in QED.







References


  1. M. Srednicki, Quantum field theory, Cambridge university press (2007).


  2. A. Zee, Quantum field theory in a nutshell, Universities press (2005).



  3. M. Kaku, Quantum field theory- a modern introduction, Oxford university press (1993).



  4. M. E. Peshkin and D. V. Schroeder, An introduction to quantum field theory, Addison-Wesley publishing company (1995).



  5. P. Ramond, Field theory : a modern primer, Addison-Wesley publishing company (1990).



  6. L. S. Brown, Quantum field theory, Cambridge university press (1994).



  7. A. Lahiri and P. B. Pal, A first book of quantum field theory, Narosa (2005).





Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Elective
2 IP 3 Elective
3 MS 7 Elective
4 RS 1 Elective