6
votes
0answers
67 views

What is the intepretation of the electromagnetic tensor?

Let $A$ be the four-potential, then we know that we can form the electromagnetic tensor as $F=dA$. This is usually done as a way to have a better writing of Maxwell's equations. So, to simplify the ...
1
vote
1answer
42 views

Transformation of Electromagnetic Four-Tensor

I apologize if I am missing something obvious, but I am in my first class with tensors and I am still learning the notation. I am running into a problem with the transformation of the transformation ...
1
vote
1answer
168 views

Proving Lorentz invariance of Maxwell equations

I've read somewhere that one does not need to prove Lorentz invariance of the Maxwell equations $F_{\mu\nu,\sigma}+F_{\nu\sigma,\mu}+F_{\sigma\mu,\nu}=0$ because it is "manifestly Lorentz invariant" ...
3
votes
2answers
180 views

The signature of the metric and the definition of the electromagnetic tensor

I've read the definition of the electromagnetic field tensor to be ...
1
vote
1answer
194 views

Electromagnetic Tensor in Cylindrical Coordinates

I understand that the Electromagnetic Tensor is given by $$F^{\mu\nu}\mapsto\begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\ E_{x} & 0 & -B_{z} & B_{y}\\ E_{y} & B_{z} & ...
2
votes
0answers
131 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
130 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
107 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
720 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} = ...
3
votes
3answers
4k 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
154 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 ...
15
votes
4answers
716 views

Why do Maxwell's equations contain each of a scalar, vector, pseudovector and pseudoscalar equation?

Maxwell's equations, in differential form, are $$\left\{\begin{align} \vec\nabla\cdot\vec{E}&=~\rho/\epsilon_0,\\ \vec\nabla\times\vec B~&=~\mu_0\vec J+\epsilon_0\mu_0\frac{\partial\vec ...
2
votes
2answers
612 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 ...