Invariance for every $x$ requires
$$
\boxed{\Lambda^T\eta\Lambda=\eta},
\qquad
\eta_{\rho\sigma}\Lambda^\rho{}_\mu\Lambda^\sigma{}_\nu
=\eta_{\mu\nu}.
$$
Thus $G=O(1,3)$, the <Lorentz group>; its identity component is $SO^+(1,3)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 4 / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-302/4/i/solution