5
votes
1answer
86 views

E&M and geometry - a historical perspective

Recently, I was contemplating the beautiful formulation of electromagnetism (specifically Maxwell's equations) in terms of differential forms: $$F=\mathrm{d} A\implies \mathrm{d}F=0 ...
14
votes
2answers
368 views

Why isn't general relativity the obvious thing to try after special relativity?

To preface my question, I ask this as a mathematics student, so I don't have a very good sense of how physicists think. Here is the historical context I'm imagining (in particular taking into account ...
4
votes
3answers
1k views

Why is the symplectic manifold version of Hamiltonian mechanics used in Newtonian mechanics?

Books such as Mathematical methods of classical mechanics describe an approach to classical (Newtonian/Galilean) mechanics where Hamiltonian mechanics turn into a theory of symplectic forms on ...