Posted on March 3, 2019January 19, 2023 by 201903030456 Exercise 4.6.1 Exercise 4.6.1. Use a similar approach (involving renaming indices and grouping like terms) to prove equation 4.20. Eq. (4.20): Eq. (4.10): Then,
![\begin{aligned} \displaystyle{\frac{\mathrm{d}}{\mathrm{d}\tau}}(A^2) & = \displaystyle{\frac{\mathrm{d}}{\mathrm{d}\tau}}(\eta_{\mu\nu}A^\mu A^\nu )\\ & = \eta_{\mu\nu} \bigg[ A^{\mu}\displaystyle{\frac{\mathrm{d}}{\mathrm{d}\tau}(A^\mu )} + \displaystyle{\frac{\mathrm{d}}{\mathrm{d}\tau}}(A^\mu )\cdot A^\nu \bigg] \\ & = 2\eta_{\mu\nu}A^\mu \displaystyle{\frac{\mathrm{d}A^\nu}{\mathrm{d}\tau}} \end{aligned}](https://physicspupil.com/wp-content/ql-cache/quicklatex.com-c6983a2094eb3feb81262ee8a900e29d_l3.svg "Rendered by QuickLaTeX.com")
