All Questions
Tagged with electromagnetismconformal-field-theory
12 questions
1vote
0answers
65views
The field strength is a primary field
I've often read (and used in computations) that the field strength tensor $F_{\mu\nu}$ is a primary field. What is a straightforward way to see this? Moreover, does this property imply any ...
1vote
1answer
104views
Does the Field strength transform under a conformal transformation?
I'm trying to prove that the Maxwell action $$S = -\frac{1}{4}\int d^d x \; F_{\mu\nu} F^{\mu\nu}$$ is conformally invariant only if $d=4$. For this I read this question that argues that the integrand ...
1vote
1answer
156views
Proving the Maxwell action is conformally invariant
I want to show that the Maxwell action $$S = -\frac{1}{4}\int d^4 x F_{\mu\nu} F^{\mu\nu}$$ is invariant under conformal transformations in $d=4$. For this I considered the proof given in Zee's book ...
0votes
1answer
200views
Electromagnetic tensor in a FRW metric
In some papers [like https://arxiv.org/pdf/2204.06883.pdf, eq. (31) ], I see that the Electromagnetic tensor field, for a FRW metric (written in a conformal way) \begin{equation} ds^{2} = a^{2}(\tau) \...
- 369
0votes
1answer
737views
Electric field produced by a capacitor consisting of two parallel plates of different lengths: field lines and edge effect
It is known that the following integral equation describes the electrostatic field produced by a capacitor consisting of two parallel circular plates, derived in this paper (download for free) $$f(x)...
- 163
0votes
1answer
66views
Dilatations and action on derivatives of fields
How do derivatives of fields transform under dilatations? Specifically I am interested on what I misunderstand with the example: Consider a theory that has a field $A_\mu$ that transforms under ...
- 121
3votes
1answer
2kviews
What is the significance of the conformal invariance of electrodynamics in a covariant formulation?
I am a confused about the role of symmetry transformations in a covariant formulation. Maxwell's equations can be shown to be invariant under conformal transformations. See e.g. here: https://arxiv....
- 234
11votes
0answers
663views
Special conformal transformations and image charges
Let us consider a grounded conducting sphere with radius $r$ and a point charge $e$ at a distance $R>r$ from the center of the sphere. For simplicity, we can choose the sphere centered at the ...
- 673
2votes
0answers
308views
Conformal transformation: electric field of dipole
In beautiful paper (open access) authors calculate analytically optical response of "kissing" nanowires. Authors use method of "conformal transformation". Firstly, authors consider dipole (dipole ...
- 369
11votes
1answer
1kviews
Conformal invariance of Electromagnetic field action
What is the significance of Conformal invariance of Electromagnetic field action? What does it lead to? And how can we break it?
- 1,145
3votes
0answers
1kviews
Is classical electromagnetism conformally invariant? (and a bit of general covariance)
The contest is a flat $4d$ Minkowsky space. A conformal transformation is a diffeomorphism $\tilde x(x)$ such that the metric transforms as \begin{equation*} \tilde g_{\tilde \mu \tilde \nu} = w^2(x) ...
- 616
3votes
2answers
2kviews
Invariance of Maxwell's Equations under inverting variables - Reference and use
Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
