All Questions
Tagged with duality electromagnetism
42
questions
1
vote
1
answer
81
views
Electromagnetic duality and vector/pseudovector transformation properties
One consequence of electromagnetic duality (see e.g., https://doi.org/10.1038/s41467-023-36420-4) is that if we have a system described by permittivity and permeability profile $(\varepsilon, \mu)(\...
- 136
1
vote
0
answers
39
views
Reference for dual gauge field and magnetic field being canonically conjugate
The gauge field operator in quantum Yang-Mills is canonically conjugate to the electric field.
I know that the dual gauge field is canonically conjugate to the magnetic field, but I can't seem to dig ...
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:
$$\mathcal{L} = - \frac{1}{4} F_{\mu\nu} F^{\mu\nu},$...
- 513
2
votes
1
answer
209
views
Is the Dirac monopole quantization condition out by 1/2?
Consider an electron with electric charge $e$ that is moved around a closed horizontal circular path $C$ centered around a magnetic monopole with magnetic charge $g$. Assume that the monopole produces ...
- 5,925
0
votes
1
answer
181
views
Why can't the electromagnetic duality transformation be expressed in terms of potentials?
In Is it possible to elevate the electric-magnetic duality discrete symmetry to a continuous one? the OP asks about how to derive the Noether current associated with the electromagnetic duality ...
- 6,601
1
vote
2
answers
153
views
Is it possible to elevate the electric-magnetic duality discrete symmetry to a continuous one?
I'm familiar with Electric-Magnetic duality, where in the absence of source fields one can exchange the $F_{\mu \nu}$ field with the dual field: $\tilde{F}_{\mu \nu}={\epsilon}_{\mu \nu \alpha \beta}
...
- 1,268
2
votes
0
answers
76
views
Are we sure that electric “monopoles” are not just ends of an “Electrical Dirac String”? [closed]
The Dirac String is used to model magnetic monopoles. So how are we sure that physical electric “monopoles” are not in fact the ends of an “Electrical Dirac String” produced by a solenoid carrying a ...
- 129
2
votes
0
answers
67
views
How to identify the dyon being condensated at the ${\cal N}=2$ SUSY $u$-plane?
For the $u$-plane monodromy at $u=u_0$
$$\mathcal{M}^{p,q}=\begin{pmatrix}
1+pq & p^2 \\
-q^2 & 1-pq \\
\end{pmatrix}$$
the statement is that dyons with electric and magnetic charges $(p,q)$ ...
- 169
2
votes
0
answers
136
views
Photon propagators in self-dual electromagnetism
$\quad$Consider extending Maxwell electromagnetism with the dual photon field $\tilde{A}$.
The complex combinations $A^\pm = \frac{1}{2}(A \pm i\tilde{A})$ then serve as the potentials of the self-...
- 564
2
votes
1
answer
170
views
What would happen if the fine structure constant were set to 1?
While reading up on magnetic monopoles, I have been led to understand that, due to S-duality, the magnetic equivalent of the fine-structure constant, $\alpha_M$ must be related to the reciprocal of $\...
- 2,196
2
votes
0
answers
35
views
If magnetic monopoles existed, would the electric field also require a vector potential? [duplicate]
I'm studying magnetic duality and it seems that duality is nearly complete for the exception of the apparent non-existence of magnetic monopoles.
My issue here isn't this one. My issue is that, if ...
- 223
6
votes
1
answer
287
views
Why is the electromagnetic duality an S-duality?
One of the examples that Wikipedia gives of S-duality is the EM duality. Namely that
$$
\begin{align}
\mathbf{E} &\rightarrow\mathbf{B} \\
\mathbf{B} &\rightarrow -\frac{1}{c^2}\mathbf{E} \...
- 1,544
2
votes
1
answer
280
views
Electromagnetic duality interacting with a complex scalar field
My question refers to example theory introduced in the book "Supergravity" from D.Z.Freedman & A. van Proeyen p.80. Its Lagrangian is given by
$${\cal L}(Z,F) =-\frac{1}{4}(Im Z)F_{\mu\...
- 9,778
2
votes
2
answers
246
views
Can we define a vector potential for $E$-Field in Empty Space?
In deriving the Electromagnetic wave equation in free space we remove all charge sources. The resultant Maxwell vector equations are thus source-free. Using Gaussian units with the speed of light $c=1$...
- 1,577
1
vote
3
answers
296
views
Dual EM field in terms of original EM field [closed]
In Maxwell theory we have dual description in terms of dual fields:
$$
\tilde{F}_{\mu\nu} = \partial_\mu \tilde{A}_\nu - \partial_\nu \tilde{A}_\mu
=
\varepsilon_{\mu\nu\rho\sigma} F^{\rho\sigma}
$$
$...
- 5,707