Electromagnetic tensor Definition and 21 Threads

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...

How exactly is the EM field tensor related to the proper orthochronous Lorentz group?

*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...

Hey, does anoyone of you know to which vector space the electromagnetic tensor belongs to? thank you for your ideas...

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...