What is Electromagnetic tensor: Definition and 21 Discussions
In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely.
I'm currently studying the covariant formulation of electromagnetism for a research project I'm doing and I'm a bit a stuck on how to perform the 3+1 split of the Electromagnetic Field Tensor and Maxwell's Equations.
I understand that a 3+1 split of a four-vector consists of separating the...
Following from Wikipedia, the covariant formulation of electromagnetic field involves postulating an electromagnetic field tensor(Faraday 2-form) F such that
F=dA
where A is a 1-form, which makes F an exact differential form. However, is there any specific reason for expecting F to be exact...
I've already made a post about this topic here, but I realized that I didn't understand the explanation on that post. in Chapter 7 of Rindler's book on relativity, in section about electromagnetic field tensor, he states that
_and introducing a factor 1/c for later convenience, we can ‘guess’...
I derive the quadratic form of Dirac equation as follows
$$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbrace\psi=0$$
And I need to find the form of the spin dependent term to get the final expression
$$g...
Consider equation (2.7.8) page 42 in the book Gravitation and Cosmology by Weinberg
F' αβ = Λαγ Λβδ Fγδ
Now consider the time reversal Lorenz transformation
Λμν = 0 if μ ≠ ν, 1 if μ = ν = 1..3 and -1 if μ = ν = 0
then
F' 00 = 0
F' 0i = -F 0i
F' ij = F ij
Using equation (2.7.5) of the same book...
Homework Statement
Given an electromagnetic tensor ##F^{\mu\nu}##, showing that:
$$\det{F^{\mu}}_\nu=-(\vec{B}\cdot\vec{E})^2$$
Homework Equations
The Attempt at a Solution
I had only the (stupid) idea of writing explictly the matrix associated with the electromagnetic tensor and calculating...
Can anyone help me find any mistake in this expansion ? (I've asked it also in other places but I got no answer))
Pα= e Fαβ Uβ
c = speed of light
m = "rest" mass
e = charge
a = sqr(1 - v2/c2)
v2 = vx2 + vy2 + vz2
dτ = dt a (proper time)
momentum 4 vector : Pα = [mc/a , mvx/a , mvy/a ...
Hello, first off, I'm not sure if I put this question in the right place so sorry about that.
Given Bi = 1/2 εijk Fjk how would you find F in terms of B? I think you multiply through by another Levi-Civita, but then I don't know what to do after that. Any help would much appreciated.
Hi there,
Over the last couple of weeks, I have been learning about the relativistic description of electromagnetism through Leonard Susskind's Theoretical Minimum lectures, and although I have managed to follow it, there are some parts which I am becoming increasingly confused by, not helped...
From introductory courses on EM, I was given 'sketchy' proofs that, in a EM field in vacuum, magnetic energy density is B² and electric energy density is E² (bar annoying multiplication factors; they just get under my skin, I'll skip them all in the following). Other facts of life: -FμνFμν, the...
*Edit: I noticed I may have posted this question on the wrong forum... if this is the case, could you please move it for me instead of deleting? thanks! :)
Hello, I am having problems on building my electromagnetic tensor from a four-potential. I suspect my calculations are not right. Here are...
I understand that the EM tensor is a way of expressing the electromagnetic field in a frame invariant way, but how is it derived? Please use the (-+++) convention as I mostly use that.
A while back (thread) you guys helped me understand why \tilde{F}=m\frac{d\gamma\tilde{v}}{dt} (3-vectors) as it follows from \bar{F}=q\Psi\bar{v} (4-vectors) and \tilde{F}=q(\tilde{E}+\tilde{v}\times \tilde{B}) (3-vectors). However, I had the impression that one also uses...
dear all,
I have a question about Electromagnetic field tensor.
As I was reading introduction to relativity by Hobson, I saw this sentence:
"in order that the rest mass of a particle is not altered by the action of the erforce we require the latter to be a pure force, so:
u.f=0
1) what does it...
I can find the metric tensor in cylindrical coordinates to be [1,-1,-1/r^2,-1] but how about the electromagnetic field tensor and thus the energy stress tensor?
Is it just change the Ex,Ey,Ez to Eρ,Eθ,Ez?
Is FσρFσρ still equal to 2(B^2-E^2)
Homework Statement
Using the transform of the electromagnetic tensor F between frames,
F'=RFR^{T}
verify that:
i) the perpendicular component of the magnetic field in the frame, S', moving with velocity v with respect to the frame S, can be found from the transform of B_{\bot} in S...
Homework Statement
Given: electromagnetic tensor F(superscript)uv:
electromagnetic tensor F' after the lorentz transformation:
[ 0 -Ex -gamma(Ey-VBz/c) -gamma(Ez-VBy/c)
Ex 0...
I understand that after writing down this:
F^{ \mu v} = \partial^{\mu} A^v- \partial^v A^{\mu}
We can get a nice matrix connecting E and B vectors. But I just wonder what we need this matrix for? I am a little bit confused about all this relativity in electromagnetism...
And another...
Homework Statement
Hi,
I have to calculate the invariant: \tilde{F}^{\mu \nu} \, F_{\mu \nu}
where F is the electromagnetic field tensor and \tilde{F} the dual one.
Homework Equations
First, the contravariant components of the electromagnetic field tensor are given by...