Quantum Field Theory: Lecture Log

Navigation: Fall, Spring, Last regular lecture.

QFT 1, Fall 2024 semester

Tentative plan for August 26 (Monday):

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.

Tentative plan for August 28 (Wednesday):

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.