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Quantum Field Theory

January – May 2024

This is an introductory graduate course on quantum field theory. It starts with the basic principles of the subject while also developing more advanced material. Topics include the need for fields, canonical quantization, particles, perturbation theory, Feynman diagrams, properties of the S-matrix, renormalization, functional methods and gauge theories.

The principal references are An Introduction to Quantum Field Theory by Michael Peskin and Daniel Schroeder, Volumes I and II of Steven Weinberg’s The Quantum Theory of Fields, and the notes from Sidney Coleman’s Physics 253a.

Video playlist
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View the complete playlist on YouTube

Lectures
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The topic titles below provide a short guide to the contents of each lecture.

Lecture Topic Date
1 Introduction: why relativity requires fields and infinitely many degrees of freedom 8 January 2024
2 Classical scalar fields and the Klein–Gordon equation 10 January 2024
3 Canonical quantization of the scalar field 15 January 2024
4 Particles, states and the Schrödinger functional representation 17 January 2024
5 Locality, causality and Noether’s theorem 22 January 2024
6 Noether currents, the stress tensor and local observables 22 January 2024
7 Lorentz symmetry and internal symmetries 24 January 2024
8 The S-matrix and the interaction picture 29 January 2024
9 The Dyson series, Wick’s theorem and contractions 12 February 2024
10 Propagators and the prescription 14 February 2024
11 Introduction to Feynman diagrams 19 February 2024
12 Feynman diagrams continued 19 February 2024
13 Scattering amplitudes and the Yukawa potential 21 February 2024
14 Crossing symmetry and Mandelstam variables 28 February 2024
15 Probabilities, wave packets and scattering cross-sections 4 March 2024
16 The interacting vacuum and correlation functions 6 March 2024
17 Green’s functions and introduction to LSZ reduction 11 March 2024
18 The LSZ reduction formula 12 March 2024
19 LSZ reduction, wavefunction renormalization and ultraviolet divergences 13 March 2024
20 Effective field theory and renormalization conditions 18 March 2024
21 One-loop renormalization of scalar field theory 20 March 2024
22 Counterterms, regularization and beta functions 27 March 2024
23 Duality I: the quantum Ising model and its path integral
Guest lecture by Subhro Bhattacharjee
3 April 2024
24 Duality II: from the Ising model to lattice gauge theory
Guest lecture by Subhro Bhattacharjee
8 April 2024
25 Renormalization-group flows and beta functions 15 April 2024
26 Path integrals in quantum mechanics and field theory 17 April 2024
27 Correlation functions and perturbation theory from path integrals 22 April 2024
28 Scalar electrodynamics and gauge symmetry 24 April 2024