- #1
Gene Naden
- 321
- 64
So the Euler-Lagrange equations give ##\partial _\mu ( \partial ^\mu A^\nu - \partial ^\nu A^\mu ) = J^\nu## with ##B=\nabla \times A##. I want to convert this to ##\nabla \times B - \frac{\partial E}{\partial t} = \vec{j}##. I reckon I am supposed to use the Minkowski metric to raise or lower indices, but am not sure how. I want to get from ##(\partial ^\mu A^\nu - \partial ^\nu A^\mu ) ## to ##\nabla \times A##.