Comparison of $U[\Lambda_c]$ with the operator group commutator gives the <Lorentz algebra>
$$
\boxed{
[M^{\mu\nu},M^{\rho\sigma}]
=\eta^{\nu\rho}M^{\mu\sigma}
-\eta^{\mu\rho}M^{\nu\sigma}
-\eta^{\nu\sigma}M^{\mu\rho}
+\eta^{\mu\sigma}M^{\nu\rho}}.
$$
There is no factor of $i$ because the generators are anti-Hermitian.

Solution

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

 Solution

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