All Questions
22
questions
2
votes
1
answer
65
views
Canonical electromagnetic stress-energy-momentum tensor
I have canonical electromagnetic stress-energy-momentum tensor defined as:
$T_{\mu\nu}=\frac{1}{4}\eta^{\mu\nu}F_{\alpha\beta}F^{\alpha\beta}-F^{\mu\lambda}F^{\nu}_{\,\,\lambda}-F^{\mu\lambda}\...
- 23
1
vote
0
answers
40
views
Detailed derivation of the energy-momentum tensor from the Maxwell Lagrangian [duplicate]
I have started studying QFT, and I am currently reviewing briefly on the classical field theory. I have come across the Maxwell Lagrangian given by
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}.
$$
...
- 35
1
vote
2
answers
298
views
Energy-Momentum-Tensor of classical electrodynamics is conserved
I want to check if the energy momentum tensor of the classical electrodynamics with lagrangian
\begin{align}
L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}
\end{align}
is conserved. The energy momentum tensor ...
- 505
0
votes
1
answer
50
views
Computations with Tensors
I have the following ansatz
$$T^{\mu\nu}=AF^{\mu\alpha}F_{\alpha}^\nu+B\eta^{\mu\nu}F^{\alpha\beta}F_{\alpha\beta}$$
for some constants $A,B.$ Here, $F_{\mu\nu}$ is the electromagnetic field tensor, ...
- 101
1
vote
4
answers
432
views
How to see that the electromagnetic stress-energy tensor satisfies the null energy condition?
I am trying to show that the Maxwell stress-energy tensor,
$$T_{\mu\nu} = \frac{1}{4\pi}\left( F_{\mu\rho} F^{\rho}{}_{\nu} - \frac{1}{4}\eta_{\mu\nu}F_{\rho \sigma} F^{\rho\sigma} \right),$$
...
- 857
0
votes
1
answer
218
views
Problem 2.1(b) in Peskin and Schroeder's Introduction to QFT
In this exercise the author claims that adding $\partial_\sigma K^{\sigma \mu \nu}$ does not affect the divergence of $T^{\mu\nu}$. In other words the author claims that $\partial_\mu \partial_\sigma ...
user261609
0
votes
1
answer
70
views
The variation of the Lagrangian density for the canonical energy-momentum tensor
I expanded the Lagrangian to this form
$$ \mathcal{L} = -{1 \over 4} F^{\mu \nu} F_{\mu \nu} = ... = - {1 \over 2} (\partial^{\mu} A^{\nu} \partial_{\mu} A_{\nu} - \partial^{\mu} A^{\nu} \partial_{\nu}...
- 51
3
votes
1
answer
1k
views
Maxwell stress tensor for electromagnetic wave
Sorry if this is a naive question but I've been struggling in trying to proof this for a week. Consider an electromagnetic wave with wave vector $\vec{k}=k\hat{n}$, the Maxwell stress tensor can be ...
- 1,172
0
votes
0
answers
84
views
Sign problem in electromagnetic stress energy tensor
I'm having a silly problem in calculating the electromagnetic stress energy tensor: the Lagrangian is
$$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} $$
and the stress energy tensor reads
$$ T^{\mu\...
- 4,736
0
votes
0
answers
589
views
Stress-energy tensor of the EM field has zero trace
The stress energy-tensor in EM is defined by
$$T^{\mu \nu} = -\frac{1}{4\pi}\left(E^\mu_\rho E^{\nu\rho} - \frac{1}{4} g^{\mu\nu}E_{\rho\sigma}E^{\rho\sigma}\right)$$
I aim to show one of the ...
- 172
0
votes
0
answers
56
views
Energy Stored in Electromagnetic field using Lagrangian formalism
How to we get to
$$ \int( (ɛ/2)E.E + (1/2μ)B.B ) d^{3}x $$
as the energy stored in electromagnetic field, while using the Lagrangian formalism of maxwell theory.
0
votes
2
answers
2k
views
Plate capacitor: Maxwell stress tensor and forces
I've got a plate capacitor with infinitely large plates at $z_1=d/2$ and $z_2=-d/2$. The plate at $z_1$ has a surface charge density of $\sigma$. The plate at $z_2$ has a surface charge density of $-\...
user164828
0
votes
1
answer
111
views
Conservation of stress energy
I want to show $\nabla_m T_{mn}=0$.
For this I have
\begin{align}
\nabla _m T_{mn}&=\nabla_m({F_m}^aF_{na}-\frac{1}{4}g_{mn}F_{ab}F^{ab})\\
&=(\nabla_m{F_m}^a)F_{na}+{F_m}^a(\nabla_mF_{na})-\...
0
votes
0
answers
26
views
Derivative of $T^{\mu \nu}_{\mathrm{mat}}$ in terms of $F^{\mu \nu}$ and $j^\nu$ [duplicate]
A friend of mine encountered a problem while studying GR. I'm going to answer it myself if I get some time, but here it is.
The (symmetrized) energy-momentum tensor for the electromagnetic field is $$...
user20250
0
votes
1
answer
1k
views
Evaluating the components of Maxwell's stress tensor
I was going through the Maxwell's stress tensor section of Introduction to Electrodynamics by Griffiths. In the example 8.2(screenshot below),
I fail to understand how the equation 8.23 (in the ...
- 25