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…
Not at all. To the audience the blog is written for, the article is very sensible. When two folks who know computers quite well discuss some esoteric issue, they will use technical language and assume a certain level of…
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…
Dr. Woit's blog is directed towards physicists, for the most part. This sort of thing is covered very early on in a graduate education in physics; it's old hat for that crew, but incomprehensible to anybody else!
This sort of business is covered in any textbook on quantum mechanics worth its salt. The idea goes something like this: physics should certainly not depend on where you are at or the orientation of your measuring…
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…
Not at all. To the audience the blog is written for, the article is very sensible. When two folks who know computers quite well discuss some esoteric issue, they will use technical language and assume a certain level of…
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…
Dr. Woit's blog is directed towards physicists, for the most part. This sort of thing is covered very early on in a graduate education in physics; it's old hat for that crew, but incomprehensible to anybody else!
This sort of business is covered in any textbook on quantum mechanics worth its salt. The idea goes something like this: physics should certainly not depend on where you are at or the orientation of your measuring…