1. Classical field theory Lagrangian. Hamiltonian. Field equations. Symmetries and conservation laws. 2. Canonical quantization of the Klein-Gordon field Real and complex scalar fields. Commutation relations. The Klein-Gordon propagator. 3. Canonical quantization of the Dirac field Anticommutation relations. The Dirac propagaror. Lorentz and discrete simetries (CPT). 4. Canonical quantization of the electromagnetic field Quantization in the Lorentz and Coulomb gauge. The photon propagator. 5. Perturbation theory Wick's theorem. Feynman diagrams. Cross section and the S matrix. Examples: phy(4) and QED. 6. QED processes e(+) e(-) -> mu(+) mu(-). Compton Scattering. Pair creation. Electron scattering in an external field. Scattering of the polarized particles. 7. Path integral in quantum mechanics Hamiltonian and Lagrangian path integral. The vacuum to vacuum transition amplitude. Functional derivatives. Green functions. 8. Functional quantization of the scalar field The free scalar theory. Interacting theory [phi(4) theory]. Generating functionals of Green functions. The effective action and 1PI functions. Feynman rules. Schwinger-Dyson equations. 9. Functional quantization of the electromagnetic field Faddeev-Popov method. Propagators. 10. Functional quantization of the Dirac field Grassmann variables. Integrals and derivatives. Generating functional of the Dirac field. The Dirac propagator. QED. 11. Radiative corrections The electron vertex function. Anomalous magnetic moment. Pauli-Villars regularization. Spectral representation. The LSZ reduction formulas. Self energy of the electron. The optical theorem. Ward identity. The photon self energy (dimensional regularization). Lamb shift. The infrared divergence. 12. Renormalization Counting of UV divergences. Renormalization of the phy(4) theory and QED. t'Hoft's approach to the RG equations. Callan-Symanzik equation. Computation of beta and gamma functions in the MS scheme. The effective coupling constant. Asymptotic freedom.
Requirements include: 1 seminar Literature: 1. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Addison Wesley, 1995 2. F. Mandl and G. Show, Quantum Field Theory, New York, 1984 3. P. Ramond, Field Theory: A Modern Primer (second edition), Addison-Wesley, RedwoodCity, California, 1989 4. W. Greiner and J, Reinhardt, Field Quantization, Springer, Berlin, Heidelberg, New York, 1996 5. D. Bailin and A. Love, Introduction to Gauge Field Theory, Adam Hilger, Bristol, 1986 6. L. Ryder, Quantum Field Theory, Cambridge University Press, Cambridge, 1985. 7. V. Radovanovic, Problem Book in Quantum Field Theory, Belgrade, 2001 (in Serbian)
This course is followed by Quantum Gauge Field Theory
