Linked Questions
10 questions linked to/from Electrodynamics and the Lagrangian density
52
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5
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Derivation of Maxwell's equations from field tensor lagrangian
I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$...
amc
7
votes
1
answer
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Retrieving Maxwell's equations from the minimum action principle
I'm currently working at the start of Alexei Tsvelik's book Quantum Field Theory in Condensed Matter Physics. I'm kinda stumped on a few essential steps.
Starting with the action:
$$S = \int dt \int ...
- 1,062
2
votes
2
answers
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Deriving Euler-Lagrange for Electrodynamics Lagrangian [duplicate]
For $\mathcal L = -\frac14 F_{\mu\nu}F^{\mu\nu}$ I would appreciate some help evaluating
$$\frac{\partial \mathcal L}{\partial(\partial_{\mu}A_{\nu})}.$$
I've found
$$\frac{\partial \mathcal L}{\...
- 2,022
4
votes
3
answers
694
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Field equations of a given action [duplicate]
Provided an action:
$$S[A_\nu] = \int\left(\frac{1}{4\mu_0}(A_{\gamma,\mu}-A_{\mu,\gamma})(A_{\zeta,\alpha}-A_{\alpha,\zeta})\eta^{\gamma\zeta}\eta^{\mu\alpha}+\frac{1}{2}\nu^2A_\mu A_\gamma -\beta A_\...
- 43
1
vote
1
answer
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Variation of electromagnetic action to obtain Maxwell's equations
The electromagnetic action is given in the language of differential forms by
$$S[A]=-\frac{1}{4}\int F\wedge \star F$$
The variation of the electromagnetic action $S$ gives us Maxwell's equations
$$d\...
- 3,243
1
vote
1
answer
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Euler-Lagrange Equation Proving Maxwell Equation [duplicate]
When quantizing the EM Field, we get the Lagrangian density,
$$L=\frac{1}{2}\left(\epsilon \vert E\vert ^2 - \frac{1}{\mu}\vert B\vert^2\right) = \frac{\epsilon}{2}\vert\nabla\phi + \dot{\textbf{A}}\...
- 1,951
1
vote
1
answer
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Calculating Lagrangian of electromagnetism [duplicate]
I know that the interaction terms of the Lagrangian of electromagnetism are given by
$$L_{int}=-q\phi (\mathbf{x},t)+q\mathbf{v}(t)\cdot \mathbf{A}(\mathbf{x},t).$$
The above equation is replaced by ...
- 233
1
vote
1
answer
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Finding the magnetic vector potential by calculus of variations
Given the functional $$F[A]=\int_{\mathbb{R}^3}\{\frac{1}{2\mu(x)}|\nabla\times\vec{A}|^2-\vec{J}\cdot\vec{A}\}d^3x$$ with $\vec{A}$ is a candidate vector potential for the field $\vec{B}=\nabla\times\...
- 53
2
votes
1
answer
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Derivatives with Two Indices in Electromagnetic Lagrangian [duplicate]
I was reading about the derivation of Maxwell's equations from an electromagnetic Lagrangian density from Sean Carroll's Spacetime and Geometry: An Introduction to General Relativity. The Lagrangian ...
- 3,043
0
votes
0
answers
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Euler-Lagrange Equations for EM Field Theory [duplicate]
Suppose that you have the Lagrangian density for $\phi(\vec{x}, t)$ and $\vec{A}(\vec{x}, t)$ given as follows:
$$\mathcal{L} = \frac{\epsilon_{0}}{2} |-\nabla\phi - \partial_{t}\vec{A}|^{2} - \frac{1}...
- 299