- #1

yancey

- 11

- 0

##L=Const.{\times}F^{\mu\nu}F_{\mu\nu}##, where

[itex]F_{\mu\nu}=({\partial}_{\mu}-{\alpha}{\partial}^{\rho}{\partial}_{\rho}{\partial}_{\mu})A_{\nu}-({\partial}_{\nu}-{\alpha}{\partial}^{\rho}{\partial}_{\rho}{\partial}_{\nu})A_{\mu}[/itex]. Now I will apply the least action principle to it. Which one of the following two choices is the right one?

[itex]{\delta}S=\frac{{\partial}S}{{\partial}A_{\mu}}{\delta}A_{\mu}+\frac{{\partial}S}{{\partial}({\partial}_{\mu}A_{\nu})}{\delta}({\partial}_{\mu}A_{\nu})=0,[/itex]

or

[itex]{\delta}S=\frac{{\partial}S}{{\partial}A_{\mu}}{\delta}A_{\mu}+\frac{{\partial}S}{{\partial}({\partial}_{\mu}A_{\nu})}{\delta}({\partial}_{\mu}A_{\nu})+\frac{{\partial}S}{{\partial}({\partial}_{\mu}{\partial}_{\nu}{\partial}_{\rho}A_{\lambda})}{\delta}({\partial}_{\mu}{\partial}_{\nu}{\partial}_{\rho}A_{\lambda})=0.[/itex]