i was reading a paper and i find something that i don't understand.
This is the paper "An action principle for action-dependent Lagrangians: Toward an action principle to non-conservative systems".
In the theorem II.1 the author writes. Let $\partial_{\mu}L=\gamma_{\mu}$ be a gradient $\gamma_{\mu}=\partial_{\mu}f(x^{v})$ (1). The indexes in the left hand side of the equation (1) are correct?
Can you give a place to read about this or one example?
Thank you.