8.3 Internal and space-time symmetries

Above I have mentioned angular momentum, the vector product of position and momentum. This is defined in terms of properties of space (or to be more generous, of space-time). But we know that many particles carry the spin of the particle to form the total angular momentum,

The invariance of the dynamics is such that $J$ is the conserved quantity, which means that we should not just rotate in ordinary space, but in the abstract “intrinsic space” where $S$ is defined. This is something that will occur several times again, where a symmetry has a combination of a space-time and intrinsic part.