Linked Questions
10 questions linked to/from Physical interpretation of 2-forms dual to pseudovectors
54
votes
5
answers
6k
views
When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?
My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an equation,...
- 11.6k
19
votes
4
answers
6k
views
What is intuitively the Hodge dual of a $p$-form?
Carroll in his textbook "Spacetime and geometry" defines the Hodge dual of a $p$-form $A$ on an $n$-dimensional manifold as $$(\star A)_{\mu_1...\mu_{n-p}}=\dfrac{1}{p!}\epsilon^{\nu_1...\nu_p} _{\ \ \...
- 7,860
24
votes
3
answers
5k
views
What is a dual / cotangent space?
Dual spaces are home to bras in quantum mechanics; cotangent spaces are home to linear maps in the tensor formalism of general relativity. After taking courses in these two subjects, I've still never ...
- 1,048
10
votes
2
answers
11k
views
Significance of the Dual Electromagnetic Tensor $\tilde{\mathbf{F}}$/its derivation
In the context of Maxwell's equations, I was wondering whether there was any physical significance to the dual EM Field Tensor and/or its various derivations. It has components:
$$\tilde{\textbf{F}} = ...
- 231
0
votes
1
answer
679
views
Difference between $ \ F^{\mu\nu}$ and $\tilde F_{\rho\sigma}$
$ \ F^{\mu\nu}$ and the Hodge dual $\tilde F_{\rho\sigma}$ these are two tensors, related by $\epsilon_{\rho\sigma\mu\nu }$. My question is, is there any physical difference between them( I am aware ...
- 9
4
votes
1
answer
190
views
If the world had four spatial dimensions, then area would be a tensor?
In three dimensions area is a vector because two dimensions have a direction relative to the third. If the world had four spatial dimensions then area would be a tensor?
And what form then the laws of ...
1
vote
3
answers
562
views
Why is the magnetic field $B$ a pseudo-vector?
Physically speaking, "pseudo-vectors" are vectors $v\in \mathbb{R}^3$ which transform as $ v'= (\det {R})v$ if the "system were to transform as $R\in O(3)$". However, what does ...
- 2,183
1
vote
2
answers
168
views
Confusion about the mathematical nature of Elecromagnetic tensor end the E, B fields
I have quite a lot of confusion so the question may result not totally clear cause of that. I'll take any advice to improve it and I'll try to be as clear as possible. Everything from now on is what I ...
- 2,415
0
votes
1
answer
175
views
Pseudotensors for describing physical quantities
I have been reading about tensors from Mathematical methods for Physics and Engineering, by K.F. Riley, M.P. Hobson and S.J. Bence.
And there are a couple of things i am not getting. On page 949 (...
- 475
0
votes
1
answer
139
views
Can we replace our use of cross products with the BAC-CAB rule?
A trending question here asks a question about cross products which are related to the existence of an orientation on 3D space.
At some level what we are trying to do with cross products seems to ...
- 39k