PHYS 581: Differential Geometry for Physicists

last updated: 2.38 PM, Sep 23, 2021

what From the Aharonov-Bohm effect in quantum mechanics to the curved spacetime of General Relativity, differential geometry is everywhere in physics. In this course we will explore the basics of differential geometry from a hands-on physicist's perspective and develop the necessary tools to understand the main ideas of spacetime and General Relativity.

Keywords: Vectors, matrices, tensors, and coordinates; why you need a covariant derivative; what is a metric; geometry of 2D surfaces; differentiable manifolds; what is curvature; why are differential forms so useful; selected applications (participants can decide what will be covered): spacetime as a differentiable manifold, Maxwell's equations as differential forms, curvature in General Relativity, gauge theories

when lecture: Friday, 11am, Small 122
office hours: Monday, 10-11am, Small 235
contact Jens Boos (



  1. 2021-09-03: introduction; vectors, matrices, and tensors [notes-0.pdf]
  2. 2021-09-10: vectors, covectors, matrices, and tensors [notes-1.pdf, assignment-1-v1.pdf, assignment-1-v1.tex]
  3. 2021-09-17: frames and coordinates [notes-2.pdf, assignment-2-v2.pdf, assignment-2-v2.tex]
  4. 2021-09-24: coordinates and coordinate transformations [notes-3.pdf, assignment-3-v1.pdf, assignment-3-v1.tex]

Additional reading

  1. TBA