Relativistic Mechanics and Classical Field Theory
An introduction to Special Relativity, with a variety of applications.
We begin with a gentle and thorough introduction to Special Relativity, and take some time to have fun with shapes in Minkowski space. We proceed to an advanced treatment of relativistic particles, electromagnetic fields and weak gravitational fields (to the extent that doesn’t require General Relativity). Antiparticles are introduced early on, and we put an emphasis on actions and phase space structures. We introduce the geometric concept of spinors, and the notion of spin for particles and fields. We discuss the Dirac equation and the resulting picture of the electron. We introduce conformal infinity. Time allowing, we discuss a bit of conformal field theory and some physics in de Sitter space.
Tensors in 3d: moment of inertia, Maxwell’s equations, stresses etc.
Special Relativity in 3d language.
Special Relativity in 4d language: Minkowski spacetime.
Some fun geometry in Minkowski spacetime: spheres, polyhedra etc.
Relativistic particles and antiparticles in electromagnetic and weak gravitational fields.
Phase space structure in relativistic mechanics.
Maxwell’s equations; plane waves and the electromagnetic field of point charges.
Linearized Einstein equations; plane waves and the distant gravitational field of point masses.
Relativistic thermodynamics and hydrodynamics.
Spinors in 3d and 4d.
The little group and spin for massive and massless particles.
The Dirac equation and the relativistic electron.
The conformal boundary of Minkowski spacetime.
(*) Conformal symmetry and the embedding-space formalism.
(*) An introduction to de Sitter space through the embedding-space formalism.
Midterm exam 25% (only if helps the final grade); Final exam 75%. Mandatory homework submission.
Maxwell’s equations in differential form. Solving Maxwell’s equations to obtain electromagnetic waves. Quantum mechanics.
Landau & Lifshitz vol. 2 (“Classical Theory of Fields”).
“Fields”, Warren Siegel [https://arxiv.org/abs/hep-th/9912205].
“Special Relativity”, Thomas M. Helliwell.
“Spinors and Spacetime, Vol. 1: Two-spinor Calculus and Relativistic Fields”, Roger Penrose & Wolfgang Rindler.
Alternate years course, AY2024