New answers tagged stress-energy-momentum-tensor
2
votes
Divergence of canonical energy-momentum tensor in QFT
the energy-momentun tensor I got $$ T_{\mu\nu} = \frac{\partial \mathcal{L}}{\partial(\partial^{\mu}\phi)} \partial_{\nu} \phi - \mathcal{L} g_{\mu\nu}
$$
The above equation is all you need. You do ...
- 23.3k
2
votes
Accepted
Some doubts on the derivation of $\partial_\mu T^{\mu\nu}=+\frac{1}{c}F^{\nu\sigma}J_\sigma$ for particles
First, consider the definition of the particle energy-momentum tensor, $T^{\mu\nu}_{\text{part}}(x)$. You're right to be a bit puzzled; it's not a given, but rather a construction representing the ...
- 196
1
vote
Accepted
Rules for calculating the energy-momentum tensor
In the expression $$\mathcal L_0=\frac{1}{2} g^{\alpha \beta} (\partial_\alpha \phi) (\partial_\beta \phi), $$ the indices $\alpha$ and $\beta$ are summation indices. On the other hand, in the ...
- 7,298
0
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The energy-momentum tensor is symmetric, why we have different interpretation of $T^{i0}$ and $T^{0i}$?
$T^{i0}$ energy flux , $T^{0i}$ momentum density. The Symmetry follows from the fact that energy and momentum are the same thing rewieved in different reference frames. If energy is flowing in the ...
0
votes
Landau and Lifshitz argument for symmetry of stress tensor
When you add up all the forces acting on an assembly of particles (in continuum mechanics this comes down to the net force acting on a region or a volume) the net force should be due only to the ...
5
votes
Accepted
Interpreting a constraint on a simplified static spherically symmetric metric
OP's metric is an example of ultrastatic spacetime, i.e. it is a direct product of a Riemannian manifold (“space”) and $\mathbb R$ (“time”) and thus $-g_{tt}$ can be set to unity everywhere.
This ...
- 16.6k
1
vote
Accepted
Traceless stress-energy-momentum tensor of a real scalar field theory
The trace of the energy momentum tensor is not zero for the Lagrangian you chose. If you want a traceless tensor you must use
$$
S[\varphi,g]= \frac 12 \int d^nx \sqrt{g}\left( g^{\mu\nu} \partial_\mu ...
- 56.5k
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