With cyclic spatial indices,
$$
J_1=M^{23},\quad J_2=M^{31},\quad J_3=M^{12},
\qquad K_i=M^{0i}.
$$
Substitution in the given <Poincare algebra> brackets yields
$$
[J_1,J_2]=J_3,
\qquad [J_1,K_2]=K_3,
\qquad [K_1,K_2]=-J_3.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 3 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-302/3/b/solution