Tagged Questions
6
votes
5answers
187 views
In coordinate-free relativity, how do we define a vector?
Relativity can be developed without coordinates: Laurent 1994 (SR), Winitzski 2007 (GR).
I would normally define a vector by its transformation properties: it's something whose components change ...
10
votes
3answers
325 views
Representing forces as one-forms
First of all, sorry if any of those things are silly or nonsense, I'm just trying to understand better how the concepts of forms, exterior derivative and so on can be used in physics.
This question ...
1
vote
1answer
303 views
Bra space and adjoint vectors
If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
4
votes
1answer
1k views
Uniqueness of Helmholtz decomposition?
Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that
$$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$
...
