Tagged Questions
0
votes
1answer
36 views
Zero-zero (lower indicies) term for affine connection ($\Gamma_{00}^\lambda$), why do some terms dissapear?
More simply a tensor algebra question, but in General relativity I have the following when I calculate $\Gamma_{00}^\lambda$:-
$$
\Gamma_{00}^\lambda = \frac{1}{2}g^{\nu\lambda}\left(
\frac{\partial ...
0
votes
0answers
60 views
What is mathematics (in physics) of this tensor equation? [migrated]
I want to know what is $C^{a}C_{a}$ if $C^{a}=A^{a}+B^{a}$ and $C_{a}=A_{a}+B_{a}$?
a. this one $A^{a}A_{a}+B^{a}B_{a}$ or
b. this one $(A^{a}+B^{a})(A_{a}B_{a})$
1
vote
1answer
67 views
Derivative of covariant EM tensor
I cannot seem to prove that the derivative of the duel tensor = 0.
$$ \frac{1}{2}\partial_{\alpha}\epsilon^{\alpha \beta \gamma \delta} F_{\gamma \delta} = 0. $$
Writing this out I get (for some ...
0
votes
1answer
76 views
Tensor manipulation
Having a bit of trouble applying what I know about tensor manipulation, given,
$T^{\mu \nu} = \left( g^{\mu \nu} - \frac{p^\mu n^\nu + p^\nu n^\mu}{p \cdot n} \right)$,
I need to compute quantities ...
2
votes
3answers
264 views
Maxwell Stress Tensor in the absence of a magnetic field
I'm having some trouble calculating the stress tensor in the case of a static electric field without a magnetic field. Following the derivation on Wikipedia,
Start with Lorentz force:
$$\mathbf{F} = ...
2
votes
1answer
110 views
Write $\epsilon_{\mu\nu\alpha\beta} F^{\mu\nu} F^{\alpha\beta}$ as a total divergence $\partial_\mu G^\mu$
I have the following homework problem in theoretical electrodynamics:
Show that the gauge invariant Lagrange density $\epsilon_{\mu\nu\alpha\beta} F^{\mu\nu} F^{\alpha\beta}$ can be written as a ...
