## Wednesday, April 8, 2015

### boosted electric and magnetic fields

electric and magnetic fields seem to transform into each other under Lorentz-transformation: is it possible to boost into a frame in which one type of field disappears completely?

#### 1 comment:

1. electric and magnetic fields transform into each other due to the transformation of the field tensor under Lorentz-transformations, $F_{\mu\nu}\rightarrow \Lambda_\mu^\rho\Lambda_\nu^\sigma F_{\rho\sigma}$, while the Maxwell-Lagrange density $\mathcal{L}\propto F_{\mu\nu}F^{\mu\nu}$ requires the invariance of $\vec{E}^2-\vec{B}^2$ and $\vec{E}\cdot\vec{B}$, which limits how the fields can be made to vanish in some frame.