Quantum Field Theory: Lecture Log

This is the lecture log for the Quantum Field Theory classes PHY 396 K and PHY 396 L taught in 2026/27 by professor Vadim Kaplunovsky.

Most lectures should be video recorded and the records available on Canvas. For the few lectures that did not get recorded because of technical glitches, I shall scan the notes I have used in class and links the scans to this page.

Navigation: Fall, Spring, Last regular lecture.

QFT 1, Fall 2026 semester

August 25 (Tuesday):

Syllabus and admin: course content, textbooks, prerequisites, homework, exams and grades, etc.
General introduction: reasons for QFT; field-particle duality.
Lagrangian mechanics: Lagrangian and action; least action principle; Euler–Lagrange equations; multiple dynamical variables; counting the degrees of freedom.
Introduction to classical fields: Definition of a classical field; Lagrangian density.

August 27 (Thursday):

Introduction to classical fields: Definition of a classical field; Lagrangian density; Euler–Lagrange equations for fields; Klein–Gordon example; multiple fields; complex fields; Landau–Ginzburg example; higher space derivatives and non-local Lagrangians for non-relativistic fields.
Relativistic fields: relativistic sign conventions; Einstein summation convention; relativistic ℒ and field equations; Klein–Gordon example; multiple scalar fields.
Relativistic electromagnetic fields: the 4–tensor F^μν=−F^νμ and the relativistic form of Maxwell equations; the 4–vector potential A^μ and the gauge transforms; the Lagrangian formulation; current conservation and gauge invariance of the action; counting the EM degrees of freedom.
Canonical quantization v. functional quantization.

Plan for September 1 (Tuesday):

Review of canonical quantization: Hamiltonian formalism in classical mechanics; quantization, operators, and commutation relations; Poisson brackets and commutator brackets.
Introduction to quantum fields: Hamiltonian formalism for the classical fields; quantum fields; equal-time commutation relations; quantum Hamiltonian, Heisenberg equtions, and the quantum Klein-Gordon equation.
Quantum fields and particles: expanding free relativistic scalar fields into modes; creation and annihilation operators for a bunch of harmonic oscillators; eigenstates of the free quantum field's Hamiltonian.

Tentative plan for September 3 (Thursday):

Finish Quantum fields and particles: identifying the identical bosons; the Fock space; Casimir effect (briefly).
General identical bosons: bosonic Fock space and its occupation number basis; creation and annihilation operators; wave-function language vs. Fock-space language; one-body operators; two-body operators; non-relativistic quantum fields; “second quantization”.
Begin Lorentz groups: rotation group SO(3); general Lorentz group O(3,1); proper and orthochronous subgroups.

QFT 2, Spring 2027 semester

Too early to plan.