All Questions
Tagged with electromagnetismfield-theory
320 questions
0votes
0answers
54views
Extra terms for electromagnetic stress-energy tensor?
I am using the following Lagrangian density for classical electrodynamics. \begin{align*} \mathcal{L} &= -\frac{1}{4\mu_0} F^{\mu\nu} F_{\mu\nu} + J^\mu A_\mu \end{align*} This gives 2 of ...
- 940
1vote
0answers
65views
The field strength is a primary field
I've often read (and used in computations) that the field strength tensor $F_{\mu\nu}$ is a primary field. What is a straightforward way to see this? Moreover, does this property imply any ...
0votes
1answer
82views
Describing photons with the Klein-Gordon equations
I am currently studying Introduction to Elementary Particles, by Griffiths, and in Chapter 7 (QED) he begins by stating there are essentially 3 equations we shall be using to describe particles: ...
- 2,164
1vote
1answer
156views
Proving the Maxwell action is conformally invariant
I want to show that the Maxwell action $$S = -\frac{1}{4}\int d^4 x F_{\mu\nu} F^{\mu\nu}$$ is invariant under conformal transformations in $d=4$. For this I considered the proof given in Zee's book ...
2votes
1answer
96views
Degrees of freedom of a massive vector field
For a vector field $A^\mu$, when we introduce a mass term, gauge invariance breaks and this leads to the appearance of a longitudinal polarization state in addition to the two transverse ones. This ...
- 1,750
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39views
Why are there constants in the Lagrangian? [duplicate]
I have a question regarding the constant terms in the lagrangian in field theory. Lets take the electromagnetic action in a vacuum for example: $$ S = \int \left( -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} \...
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0answers
60views
Using Maxwell's Equations, how do we determine the harmonic component of $E$ and $B$?
Maxwell's Equations tell us the div and curl of $E$ and $B$. But a vector field $F$ is not uniquely specified by knowing its div and curl; there is also a harmonic component (zero div, zero curl). ...
- 309
1vote
2answers
110views
Efficiently deriving Maxwell from Euler-Lagrange equations
From the Lagrangian density for electromagnetism $$\mathcal{L} = -\frac14 F_{\mu\nu} F^{\mu\nu}$$ and the Euler-Lagrange equations $$\frac{\partial \mathcal{L}}{\partial A_\alpha} = \partial_\mu \frac{...
- 3,267
1vote
1answer
75views
What's the form of EL equation for KG field with gauge covariant derivative?
In the situation when we have KG Lagrangian with normal derivative replaced by the covariant one (I'm using metric $\operatorname{diag}\{ +,-,-,- \}$ so $D_\mu = \partial_\mu + iq A_\mu,\ D^\mu = \...
- 333
1vote
0answers
55views
How to integrate out the dynamical gauge field in the relativistic Abelian-Higgs action?
I am trying to understand the effective current-current interactions that a theory with a complex scalar field generates when one integrates out a dynamical gauge field. This is in context of ...
0votes
0answers
57views
Units of the action of a charged particle in four-potential coupling
I have a question about the definition of the action that Landau defines as: \begin{equation} S= -\frac{e}{c}\int A^{\mu}dx_{\mu} \end{equation} he says that the $1/c$ factor is introduced by ...
0votes
1answer
69views
Does anyone know if a lagrangian term of the form $\mathcal{L}=\frac{g}{4}\bar{\psi}\sigma^{\mu\nu}F_{\mu \nu}\psi$ has a name?
I am currently working in a problem that involes an interaction lagrangian of the form $\mathcal{L}=\frac{g}{4}\bar{\psi}\sigma^{\mu\nu}F_{\mu \nu}\psi$ and i would like to know if it has a name so ...
- 3
0votes
1answer
86views
Why is $*F^{\mu \nu} *F_{\mu \nu}$ not considered in Lagrangian of EM?
In Lagrangian of electromagnetism $F_{\mu \nu} F^{\mu \nu}$ and $*F_{\mu \nu} F^{\mu \nu}$ are used, where the $*$ denotes Hodge dual. But $*F^{\mu \nu} *F_{\mu \nu}$ is not used, why? I know an ...
- 336
0votes
0answers
45views
What would happen, if I combined two photon beams with their electrical field components in phase, but their magnetic ones out of phase
I know very little physics, but was asking questions of an LLM to try to understand the nature of photons. This lead a thought experiment set up like this. I have a laser source, firing into a beam ...
2votes
2answers
103views
Is First-Class Constraint Generator of matter Gauge Symmetry in EM example?
In EM theory, we can find first-class primary constraint, $$\Pi^{0}(x) = 0\tag{1}$$ and first-class secondary constraint, $$\partial_{i} \Pi^{i}(x) = 0\tag{2}$$ with Lagrangian $$\mathcal{L} = -(1/4)F^...
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