David Tong: Lectures on Supersymmetric Quantum Mechanics
These are introductory lectures on supersymmetric quantum mechanics, aimed at Masters students.
They describe some applications of quantum mechanics to ideas in geometry.
The lecture notes are
around 100 pages. Please do email me if you find any typos or mistakes.
Content
- 1. Introducing Supersymmetric Quantum Mechanics:
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The supersymmetry algebra, the spectrum and ground states, the Witten index; the supersymmetric action and supersymmetry transformations, Supersymmetry, forms, spinors and holomorphy. - 2. Supersymmetry and the Path Integral:
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The partition function and the index, the harmonic oscillator, periodic and anti-periodic boundary conditions; Instantons and tunnelling, the dilute gas approximations; Instantons and supersymmetry, fermi zero modes, determinants. - 3. Supersymmetry and Geometry:
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The supersymmetric sigma model, Quantisation and forms, de Rham cohomology, the Witten index and the Chern-Gauss-Bonnet theorem; Morse theory, instantons and the Morse-Witten complex; the Atiyah-Singer index theorem.
Resources and Classic Papers
- Supersymmetry by David Skinner
- Mirror Symmetry by many authors, but Parts II and III by Kentaro Hori are particularly useful.
- Constraints on Supersymmetry Breaking by Edward Witten
- Supersymmetry and Morse Theory by Edward Witten
- Supersymmetry and the Atiyah-Singer Index Theorem by Luis Alvarez-Gaumé