The GR & QFT Seminar

The purpose of this seminar is to provide mathematicians with gentle, brief introductions to the twin pillars of 20th century physics: general relativity (GR) and quantum field theory (QFT). Mat Langford will give five lectures on GR, and John Huerta will give five lectures on QFT. We'll post the notes here in the hopes that they can benefit a larger audience, including our friends at ANU who are presently traveling.

Since we are learning as we go, any comments or corrections would be deeply appreciated! You should email Mat Langford about the GR notes, and John Huerta about QFT.

• GR Lecture 1, A Brief History of Spacetime (10th August): Mat Langford on three mathematical models for flat spacetime: Aristotlean, Galilean, and finally, Einsteinian. The structure of these spacetimes is described, as are their symmetries, with particular focus on classic results about Einsteinian (better known as Minkowski) spacetime: the Doppler effect, time dilation, and length contraction.

• QFT Lecture 1, The Harmonic Oscillator and the Free Scalar Field (17th August): John Huerta with a lightning overview of quantum mechanics, and the quantum version of the simplest physical system: the harmonic oscillator. Creation and annihilation operators are introduced and the energy spectrum derived. We then turn to the free scalar field: classically, this is a field satisfying the Klein-Gordon equation. By Fourier transforming at an instant of time, we see how to think of this field as an infinite-collection of harmonic oscillators. We quantize the field by quantizing the oscillators, and obtain the free scalar quantum field.

• GR Lecture 2, The Geometry of Minkowski Spacetime (24th August): Mat Langford talks about the geometry of special relativity, and all the classic results: length contraction, time dilation, and the twin paradox.

• QFT Lecture 2, The Mathematics of the Free Scalar Field (31st August): COMING SOON!

• GR Lecture 3, Riemann's Geometry (6th September): Mat Langford's overview of the key constructions of Riemannian geometry that we will need for general relativity.