Tagged Questions
1
vote
1answer
80 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:
$$S = \int dt \int ...
0
votes
0answers
34 views
Lagrangian of electromagnetic tensor in light cone coordinates? [closed]
I have Lagrangian Density of Electromagnetic field Tensor in light cone coordinates using D'Alembertian operator and Lagrangian density in Cartesian coordinates. I couldn't figure out the way to ...
2
votes
2answers
59 views
Where is the magnetic self energy term in $L$ for a charged particle in an electromagnetic field?
In the Lagrangian for a charged particle in an electromagnetic field
$$L = \frac{1}{2}mu^2 - q(\phi - \frac{\vec{A}}{c}\cdot \vec{u})$$
the energy of the particle is contained in the kinetic term, ...
6
votes
5answers
261 views
Form of the Classical EM Lagrangian
So I know that for an electromagnetic field in a vacuum the Lagrangian is $\mathcal L=-\frac 1 4 F^{\mu\nu} F_{\mu\nu}$, the standard model tells me this. What I want to know is if there is an ...
2
votes
2answers
158 views
Where does the mass term come from in the Proca Lagrangian?
There are many good books describing how to construct the Lagrangian for an electromagnetic field in a medium.
$$
\mathcal{L}~=~-\frac{1}{16\pi}F^{\mu\nu}F_{\mu\nu}-\frac{1}{c}j^{\nu}A_{\nu}
$$
...
0
votes
2answers
135 views
Hamiltonian and non conservative force
I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is $ \vec {A}= B/2 (-y, x, 0)$.
I know that $$H=\sum_i p_i \dot q_i -L$$ where $p_i$ is ...
2
votes
1answer
199 views
Electrodynamics and the Lagrangian density
Could anyone tell me what equations can I obtain from the Lagrangian density
$${\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 ...
1
vote
2answers
198 views
Partial derivative of Lagrangian density for vector field
The lagrangian density of a massless vector field is
$ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$, where $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$
Expanding out gives
...
1
vote
2answers
207 views
Charge, velocity-dependent potentials and Lagrangian
Given an electric charge $q$ of mass $m$ moving at a velocity ${\bf v}$ in a region containing both electric field ${\bf E}(t,x,y,z)$ and magnetic field ${\bf B}(t,x,y,z)$ (${\bf B}$ and ${\bf E}$ are ...
2
votes
2answers
1k views
Deriving Lagrangian density for electromagnetic field
In considering the (special) relativistic EM field, I understand that assuming a Lagrangian density of the form
$$\mathcal{L} =-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{1}{c}j_\mu A^\mu$$
and ...
0
votes
2answers
199 views
Advice on classes: Theoretical Mechanics vs E&M II
So I'm having a tough time deciding between courses next semester. I'm a rising 3rd year undergrad math major whose goal is to get a solid understanding of theoretical physics through advanced math ...
3
votes
2answers
77 views
A charged particle moves in a plane subject to the oscillatory potential
A charged particle moves in a plane subject to the oscillatory potential:
$U(r)=\frac{m\omega^2 r^2}{2}$
There is also a constant EM-field described by:
$\vec{A}=\frac{1}{2}[\vec{B}\times\vec{r}]$
...
1
vote
1answer
124 views
Question on 1st order Lagrangian Derivation in Faddeev-Jackiw Formalism
I'm looking at this reference (sorry it's a postscript file, but I can't find a pdf version on the web. This paper describes a similar procedure).
The topic is the Faddeev-Jackiw treatment of ...
9
votes
2answers
216 views
Motivation for Potentials
This is a hypothetical question about "pedagogy". Let's say I am trying to take someone who has just a very small amount of knowledge about Newtonian mechanics and convince them that the Lagrangian ...
2
votes
1answer
365 views
What gauge is used in the Lagrangian for a non-relativistic point particle in an electromagnetic potential
For the Lagrangian $$L = \frac{1}{2}mu^2 - q(\phi - \frac{\vec{A}}{c}\cdot \vec{u})$$ of a non-relativistic point particle in an electromagnetic potential, what gauge is used for the electromagnetic ...
12
votes
5answers
641 views
Making symmetry between E and B fields manifest in Lagrangian
Maxwell's equations are nearly symmetric between $E$ and $B$. If we add magnetic monopoles, or of course if we restrict ourselves to the sourceless case, then this symmetry is exact. This is not ...
3
votes
3answers
1k 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 = ...
