Spacetime, Geometry, Cosmology by William Lewis Burke

[Greg Bernhardt]

• Author: William Lewis Burke
• Title: Spacetime, Geometry, Cosmology
• Amazon Link: https://www.amazon.com/dp/0935702016/?tag=pfamazon01-20
• Prerequisities:
• Level:

 

[dx]

This is a truly 'modern' theoretical physics book, well written, and full of wisdom. It contains may ideas and viewpoints that are not generally known; for example, the fact that force is naturally a 1-form, and the geometric meaning of the canonical momenta of Hamiltonian mechanics. Introductory physics textbooks have a long way to catch up with how modern physicists think, and this is one of those books that does things right. The book treats special relativity, general relativity, cosmology and also the mathematics of the calculus on manifolds. I know of no better place to really understand what tangent vectors and 1-forms are, and the basic ideas of tensors and the the concept of a smooth manifold. It teaches one to think correctly about concepts which are not treated correctly by older books. One can gain a good facility with calculus on manifolds by working through this book.

 

[bcrowell]

This is a good book that helped me sort out some foundational issues I hadn't understood properly, such as the distinction between the affine-geometry notion of vectors and duals and the metric-geometry notion of inner products. It's a bit dry and mathematical, but there are many figures and examples. Burke isn't what I would call a lively writer, but he has a workmanlike style and his own interesting voice and point of view. He doesn't seem to have anything to say about the tensor notations I like best (abstract index and birdtracks/Penrose graphical), only presenting index-free and coordinate-based index notation. It's obviously a little silly to be learning cosmology from a book written in 1980. There is a good selection of homework problems; I haven't worked any of them yet, so I can't say anything about their quality.