All Questions
Tagged with lagrangian-formalism magnetic-monopoles
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How to describe the dynamics of a magnetic monopole charge in the external EM field using a Lagrangian in terms of the EM potentials?
The equation of motion of a magnetic charge in the fixed external electromagnetic field $\mathbf{E},\mathbf{B}$ is
$$
\frac{d}{dt}(\gamma m \mathbf{v})=q_m(\mathbf{B}-\mathbf{v}\times\mathbf{E}),
$$
...
- 21
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Least action principle for Dirac monopole
I want to find the Lorentz force formula for the magnetic charge through the principle of least action. The magnetic charge is introduced by Dirac adding inside the electromagnetic tensor a tensor $G^{...
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Lagrangian formulation of Maxwell's equations with magnetic monopole
If we set $\nabla \cdot {\bf B}=\rho_m$ where pm is the density of magnetic charges we lose the ability to write ${\bf B}=\nabla \times{\bf A}$ . Can we get a new Lagrangian that leads to the new ...
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Force law from Lagrangian for magnetic monopole
How to construct a Lagrangian that gives the Lorentz force law with both magnetic and electric monopole?
I got that the force will be of the form
\begin{equation}
m \frac{\mathrm{d}x^\nu}{\mathrm{d}\...
- 243
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Magnetic monopole Lagrangian and Hamiltonian
How do I find an equation analogous to
\begin{equation}
\mathcal{L}(q,\dot q)=\frac12 m \dot q ^2-q\phi+q\vec{\dot q}\cdot \vec A\quad\quad \text{where}\quad \vec B =\vec\nabla\times\vec A, \quad \vec ...
- 243
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Is there either a Lagrangian or a Hamiltonian formulation of electromagnetism with continuous distributions of magnetic monopoles?
Maxwell's equations generalize very nicely if we add in magnetic monopoles: we get
$$\begin{align*}
\partial_\mu F^{\mu \nu} &= J^\nu \\
\partial_\mu \tilde{F}^{\mu \nu} &= \tilde{J}^\nu,
\end{...
- 48.4k
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Magnetic monopoles in field theory
In standard QED, we couple the electron to electromagnetism by replacing
$$\partial_\mu \to \partial_\mu + i e A_\mu.$$
Upon taking the classical limit, we find that this gives electrons an electric ...
- 103k
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How will SR EM Lagrangian change if we find a magnetic charge?
When we introduce electromagnetic field in Special Relativity, we add a term of
$$-\frac e c A_idx^i$$
into Lagrangian. When we then derive equations of motion, we get the magnetic field that is ...
- 29.1k