Well, one of course has to make a distinction between the physical thing and the mathematical representation of said thing. The set of states which model a type of elementary particle furnish an irreducible…
Good question! What's important is that the Hamiltonian or Lagrangian has these symmetries. Particular solutions having rotational invariance may signify some nice properties of that solution, but it's quite irrelevant…
Ah, sorry about that! You're right, of course; my brain slipped a bit.
Where?
Of course! What you're looking for is Noether's theorem; this tells us that for every (continuous) symmetry of a system one may construct a conserved quantity. There are subtleties and exceptions, of course, but that's…
The system would be described by a multi-particle state, which would be reducible. Of course, Wigner's classification is just for classifying (most) elementary particles. A hydrogen atom can be considered a particle in…
It's not quite measurable; the magnetic potential is gauge invariant, which means, among a great deal many other things, that it has no well-defined measurable value. However, it is certainly physical; things like the…
Well, one of course has to make a distinction between the physical thing and the mathematical representation of said thing. The set of states which model a type of elementary particle furnish an irreducible…
Good question! What's important is that the Hamiltonian or Lagrangian has these symmetries. Particular solutions having rotational invariance may signify some nice properties of that solution, but it's quite irrelevant…
Ah, sorry about that! You're right, of course; my brain slipped a bit.
Where?
Of course! What you're looking for is Noether's theorem; this tells us that for every (continuous) symmetry of a system one may construct a conserved quantity. There are subtleties and exceptions, of course, but that's…
The system would be described by a multi-particle state, which would be reducible. Of course, Wigner's classification is just for classifying (most) elementary particles. A hydrogen atom can be considered a particle in…
It's not quite measurable; the magnetic potential is gauge invariant, which means, among a great deal many other things, that it has no well-defined measurable value. However, it is certainly physical; things like the…