Relativity and natural units. Single particle relativistic wave equation and its problems. Motivation for field interpretation.
Classical fields.
Quantization of free real scalar field. Complex scalar field. Antiparticles.
Perturbation theory and the S-matrix. Feynman rules.
Path intgral formalism. Feynman rules from path integral formalism.
Higher orders in perturbation theory. Loops. Regularization and renormalization.
Poincare group and field equations. Dirac equation for fermions.
Quantization of Dirac field. Path integral representation for Dirac fields.
Electromagnetic fields and gauge invariance.
Quantum electrodynamics.
| Lect.1 | 05.02 | Single particle relativistic wave equation and its problems. Motivation for field interpretation. | |
| Lect.2 | 12.02 | Classical fields. Lagrangian and Hamiltonian. Variational principle and Noether's theorem. | |
| Lect.3 | 17.02 | Quantization of free real scalar field. Creation and annihilation operator. Hamiltonian. Normal ordering. Fock space. | |
| Lect.4 | 19.02 | Fields in Heisenberg picture. Commutation relation and causality. Complex scalar field. Antiparticles. | |
| Lect.5 | 24.02 | Various propagators. Interaction picture. | First assignment. |
| Lect.6 | 03.03 | S matrix. Wick's theorem. | |
| Lect.7 | 05.03 | Scattering amplitude; Feynman rules. | |
| Lect.8 | 10.03 | Scattering crosssection. Decay width. | Second assignment. |
| Lect.9 | 17.03 | Path integral formalism of quantum mechanics. Path integral for scalar field theory. Time-ordered product. | |
| Lect.10 | 19.03 | Euclidean field theory. Connection with statistical mechanics. Euclidean and Feynman propagator. Wick rotation. | |
| Lect.11 | 24.03 | Functional calculus. Correlators and generating functional. | |
| Lect.12 | 26.03 | Feynman diagrams for correlators. Connected diagrams. | |
| Lect.13 | 31.03 | Higher orders: Loops. Bare and renormalized parameters. Counterterms and renormalized perturbation theory. | Third assignment. |
| Lect.14 | 07.04 | Evaluation of two-point and four-point functions. Superficial degree of divergence and renormalizability of φ4 theory. | |
| Lect.15 | 09.04 | Dimensional regularization. Renormalization prescriptions. Sliding scale. | |
| Lect.16 | 16.04 | Callan-Symanzik equation. Beta function and anomalous dimension. | |
| Lect.17 | 21.04 | RG flow and Wilsonian effective action. "Nonrenormalizable" interactions. | Fourth assignment. |
| Lect.18 | 23.04 | Optical theorem. Kallen-Lehmann representation. | |
| Lect.19 | 28.04 | S-matrix and LSZ reduction formula. | |
| Lect.20 | 30.04 | LSZ reduction (contd.). Representation of Lorentz group. Dirac Equation. | |
| Lect.21 | 05.05 | Canonical quantization of free Dirac field. Spin-Statistics theorem. | |
| Lect.22 | 07.05 | Grassmann numbers. Path integral quantization of Dirac field. Feynman propagator. | |
| Lect.23 | 12.05 | Perturbation theory with fermions. Feynman rules for Yukawa theory. | Fifth assignment. |
| Lect.24 | 14.05 | Gauge invariance and QED Lagrangian. Path integral for QED: Fadeev-Popov method. | |
| Lect.25 | 19.05 | Outline of canonical quantization of EM field. Connection with path integral form. Feynman rules for QED. | |
| Lect.26 | 26.05 | Scattering process: e+e- -> μ+μ-. One-loop renormalization of QED and the Beta function. |
The subject is pretty standard, and there are many good books which cover the subject. I list here some of the books I am looking at while preparing the lectures.
An Introduction to Quantum Field Theory, by Peskin and Schroeder. This has become the standard textbook of the subject. We will try to cover the materials in chapters 1-9 of this book, though not necessarily in the same order. Quantum Field Theory, by Ryder. A nice introduction to the subject, covering everything we will discuss (and more), and sometimes the algebra is done in detail. A First Book of Quantum Field Theory, by Lahiri and Pal. Does not discuss path integral quantization, but covers most of the other material of this course. Is written in a lucid style. If you have difficulty following Peskin and Schroeder, try this one (or Ryder). Field Theory: a Modern Primer, by Ramond. Uses only the path integral approach, and often works in Euclidean time. But has a very thorough exposition of regularization. The Quantum Theory of Fields, vol. 1, by Weinberg. Very different approach, and may be difficult for a first course, but is full of brilliant insights. Quantum Field Theory in a Nutshell, by Zee. Beautiful book discussing the physical ideas (the first three sections cover our course). Should be supplemented by another book for the formalism.
Of course, there are many other books which may be as good / better. In particular, I have heard praises of the following books (but have not looked at them myself).
Quantum Field Theory, by Srednicki. Quantum Field Theory, by Brown.