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,
(8.1) |
The invariance of the dynamics is such that is the conserved quantity, which means that we should not just rotate in ordinary space, but in the abstract “intrinsic space” where is defined. This is something that will occur several times again, where a symmetry has a combination of a space-time and intrinsic part.