Tagged Questions
1
vote
0answers
43 views
Solving the equation of relativistic motion
How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
1
vote
1answer
67 views
Derivative of covariant EM tensor
I cannot seem to prove that the derivative of the duel tensor = 0.
$$ \frac{1}{2}\partial_{\alpha}\epsilon^{\alpha \beta \gamma \delta} F_{\gamma \delta} = 0. $$
Writing this out I get (for some ...
1
vote
0answers
74 views
Einstein +Maxwell 's tensor
Why is it true that we can deduce that Einstein's GR equations coupled with Maxwell's EM equations may be written in the form $$R_{ij}=C(F_{ik}F_j^{\,\,k}-{1\over 4}g_{ij}F_{mn}F^{mn})$$
without ...
2
votes
3answers
264 views
Maxwell Stress Tensor in the absence of a magnetic field
I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia,
Start with Lorentz force:
$$\mathbf{F} = ...
2
votes
3answers
809 views
What does this quote about the four dimensional divergence of an antisymmetric tensor mean?
In the beginning, God said that the four dimensional divergence of an antisymmetric second rank tensor equals zero and there was light.
Can someone explain what is the meaning of this quote by ...
2
votes
1answer
110 views
Write $\epsilon_{\mu\nu\alpha\beta} F^{\mu\nu} F^{\alpha\beta}$ as a total divergence $\partial_\mu G^\mu$
I have the following homework problem in theoretical electrodynamics:
Show that the gauge invariant Lagrange density $\epsilon_{\mu\nu\alpha\beta} F^{\mu\nu} F^{\alpha\beta}$ can be written as a ...
8
votes
3answers
334 views
Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?
Maxwell's equations, in differential form, are
$$\vec\nabla\cdot\vec{E}=~\rho/\epsilon_0,$$
$$\vec\nabla\times\vec B~=~\mu_0\vec J+\epsilon_0\mu_0\partial\vec E/\partial t,$$
$$\vec\nabla\times\vec ...
1
vote
2answers
367 views
Tensor product notation [closed]
In the image there is a tensor product:
$$F_{\mu\nu}F^{\mu\nu}=2(B^2-\frac{E^2}{c^2})$$
It's about how this operation on the co- and contravariant field strength tensors can give one of the ...
0
votes
0answers
101 views
Book suggestion of traceless symmetric tensor representation of spherical harmonics [closed]
Earlier this week, a friend was showing me how to solve the angular part of Laplace's equation in spherical coordinates by considering traceless symmetric tensors and how it connects to spherical ...
