Recent content by Adam Marsh

For those running across this thread who might be helped by a picture, I thought I'd add the below. So the covariant derivative ##\nabla_{v}w## can be described as "the difference between ##w## and its parallel transport in the direction ##v##," and the relation...

It is actually not too difficult to directly get to the commutator definition of the Riemann tensor from the idea of parallel transport. For infinitesimal parallel transport from a point ##p## along a curve ##\varepsilon v## with tangent ##v##, the covariant derivative is defined as...

I'm not sure if this will be what you are looking for, but it certainly does the opposite of what most textbooks do: https://mathphysicsbook.com The idea behind the book is to avoid historical motivations, long proofs and derivations, and (here's where I may lose you) tools for practical...

Just to expand on the Euclidean and Hermitian angles, since complex angles can be a bit confusing: if a Hermitian (complex) inner product is defined on ##\mathbb{C}^{4}##, then the complex angle between two complex vectors ##v## and ##w## is defined as $$\cos\theta_{c}\equiv\frac{\left\langle...