Integrating by parts gives
$$
\widetilde a=-a,
\qquad
\widetilde b=-(b+c),
$$
because the $b$ and $c$ terms differ only by a total derivative. Hence
$$
\mathcal L\simeq
\widetilde a V_\nu\Box V^\nu
+\widetilde b V^\nu\partial_\nu\partial_\mu V^\mu
+m^2V^\mu V_\mu.
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 301 / 2 / a / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-301/2/a/i/solution