- #1
Oddbio
Gold Member
- 45
- 0
I am trying to show that the laplacian:
L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}
can also be represented as:
L = \frac{1}{2}(\vec{E}^{2}-\vec{B}^{2})
where F^{\mu\nu} = \partial{}^{\mu}A^{\nu} - \partial{}^{\nu}A^{\mu}
and
F_{\mu\nu} = g_{\mu\alpha}F^{\alpha\beta}g_{\beta\nu}
A is the scalar potential.
F^{\mu\nu} is the antisymmetric field strength tensor.
But I cannot see how they are able to represent the first equation as the second equation.
Any advice would really help me a lot.
L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}
can also be represented as:
L = \frac{1}{2}(\vec{E}^{2}-\vec{B}^{2})
where F^{\mu\nu} = \partial{}^{\mu}A^{\nu} - \partial{}^{\nu}A^{\mu}
and
F_{\mu\nu} = g_{\mu\alpha}F^{\alpha\beta}g_{\beta\nu}
A is the scalar potential.
F^{\mu\nu} is the antisymmetric field strength tensor.
But I cannot see how they are able to represent the first equation as the second equation.
Any advice would really help me a lot.
