Quantum Field Theory

About this programme

In this course, you will learn that all matter and its interactions can be described in terms of quantum fields. In particular you learn about the theories of quantum electrodynamics, chromodynamics (strong interactions) and the electroweak theory. You will also learn how to calculate scattering amplitudes and cross sections. The course begins with an introduction to the classical theory of fields in the Lagrangian and Hamiltonian formulations, and explores the fundamental relation between symmetries and conservation laws, as encoded in Noether's theorem. The quantum theory of fields is then developed, first, for non-interacting scalar fields, the Maxwell field and the Dirac field, clarifying the connection between quantum fields and elementary particles like photons and electrons. Then, to deal with interacting fields, the concepts of S-matrix expansion, scattering amplitudes and cross-sections, Feynman diagrams and rules, etc, are introduced and developed. Local gauge symmetry is introduced as the origin of all known interactions in nature. This directly leads to the theories of the electromagnetic force (quantum electrodynamics) and the strong nuclear force (quantum chromodynamics). To extend it to the weak force, we introduce spontaneous symmetry breaking and the Higgs mechanism as well as Yukawa couplings, and then formulate the unified electroweak theory as an SU(2)xU(1) gauge theory. Finally, we introduce path integrals (or functional integrals) as an alternative formulation of quantum field theory.