The GR & QFT Seminar
Australian National University, Second Semester 2012
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.