Tagged Questions
1
vote
1answer
99 views
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:
$$S = \int dt \int ...
4
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1answer
91 views
What is the action for an electromagnetic field if including magnetic charge
Recently, I try to write an action of an electromagnetic field with magnetic charge and quantize it. But it seems not as easy as it seems to be. Does anyone know anything or think of anything like ...
0
votes
0answers
72 views
Minimum energy magnetic field has zero current?
Following section 9.2 of Bellan's "Fundamentals of Plasma Physics" suppose we have some domain (I assume simply connected) $D$ with a magnetic field $\mathbf{B}$ inside, but no electrostatic field. ...
6
votes
4answers
253 views
Least-action classical electrodynamics without potentials
Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which ...
2
votes
1answer
215 views
Electrodynamics and the Lagrangian density
Could anyone tell me what equations can I obtain from the Lagrangian density
$${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times ...
3
votes
2answers
218 views
Must the action for a relativistic charge be a Lorentz scalar?
Page 580, Chapter 12 in Jackson's 3rd edition text carries the statement:
From the first postulate of special relativity the action integral must be a Lorentz scalar because the equations of ...
3
votes
3answers
2k views
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 = ...
