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Tagged with duality maxwell-equations
14
questions
2
votes
3
answers
366
views
Self-duality of Maxwell lagrangian in terms of magnetic gauge field
I have read at many places that the pure Maxwell theory (without any matter) is self-dual. This is the general form for Maxwell Lagrangian density:
$$\mathcal{L} = - \frac{1}{4} F_{\mu\nu} F^{\mu\nu},$...
- 513
2
votes
0
answers
136
views
Photon propagators in self-dual electromagnetism
$\quad$Consider extending Maxwell electromagnetism with the dual photon field $\tilde{A}$.
The complex combinations $A^\pm = \frac{1}{2}(A \pm i\tilde{A})$ then serve as the potentials of the self-...
- 564
2
votes
2
answers
246
views
Can we define a vector potential for $E$-Field in Empty Space?
In deriving the Electromagnetic wave equation in free space we remove all charge sources. The resultant Maxwell vector equations are thus source-free. Using Gaussian units with the speed of light $c=1$...
- 1,577
1
vote
3
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Dual EM field in terms of original EM field [closed]
In Maxwell theory we have dual description in terms of dual fields:
$$
\tilde{F}_{\mu\nu} = \partial_\mu \tilde{A}_\nu - \partial_\nu \tilde{A}_\mu
=
\varepsilon_{\mu\nu\rho\sigma} F^{\rho\sigma}
$$
$...
- 5,707
6
votes
1
answer
2k
views
Symmetry of Maxwell equations for electric-magnetic duality
According to Griffiths's book on electrodynamics, including magnetic charge the Maxwell equations become
$$
\begin{align*}
\nabla \cdot \vec{E} &= \frac{\rho_e}{\epsilon_0} &&&
\nabla ...
- 1,970
2
votes
2
answers
253
views
Physical implication of $\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\rightarrow -\textbf{E}$ invariance of the Maxwell's equations
An interesting observation to consider about the Maxwell's equation is that in absence of the sources, the equations are symmetric under the interchange $$\textbf{E}\rightarrow\textbf{B},~~\textbf{B}\...
- 26.8k
2
votes
1
answer
857
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Tensor Formulation of Maxwell's Equations
I've been reading up about the tensor formulation of Maxwell's Equations of Electromagnetism, and the derivations I have seen (found here: http://www.lecture-notes.co.uk/susskind/special-relativity/...
- 231
12
votes
3
answers
3k
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Symmetry in electricity and magnetism due to magnetic monopoles
I was wondering about the differences between electricity and magnetism in the context of Maxwell's equations. When I thought over it, I came to the conclusion that the only difference between the two ...
- 2,918
3
votes
3
answers
2k
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Why aren't Faraday's law of induction and Maxwell-Ampere's law (without sources) symmetric?
I was wondering why Faraday's law of induction and Maxwell-Ampere's law (without sources) are not totally symmetric in the sense that Maxwell-Ampere's law has a $\epsilon_0 \mu_0$ term on the right (...
- 2,077
4
votes
2
answers
505
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Classical Viewpoint on Electromagnetism
Note: This question may be difficult or impossible to answer within the rules of these forums due to its philosophical nature. I will delete the question if I am violating the rules.
Onto the ...
- 1,281
2
votes
2
answers
765
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What would Maxwell's Equations be if we had magnetic charges and magnetic currents?
Mind you, we still have electric charge and electric currents. But, what would Maxwell's equations look like if we had to take magnetic charges and magnetic currents into consideration? Would there be ...
- 1,072
2
votes
2
answers
3k
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Electromagnetism duality theorem
Concerning Electromagnetism, textbooks often refer to the Duality Theorem. Sometimes it is presented like this:
«Consider the Maxwell's Equations (with phasors) and a known field $\mathbf{E}_1$, $\...
- 767
3
votes
0
answers
2k
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Electromagnetic duality
A key aspect of modern physics is the mapping of theories or different descriptions of a theory into a one-to-one correspondence. As I am trying to further understand the electromagnetic field tensor, ...
- 722
3
votes
2
answers
2k
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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 ...
- 817