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Jul
23
comment Why is particle number conserved, and what are the bounds on non-conservation?
@JohnRennie: Yes, exactly. In general, this would violate energy conservation event-by-event (although there might be a loophole). You can turn it around: if nature is strictly local, and all information is in the wavefunction, how does nature ensure conservation of energy? I'm pretty sure it does of course, but it's a non-trivial question.
Jul
23
revised Show that charge conservation $\partial_\mu J^\mu = 0$ implies global U(1) invariance?
I renamed the other question, because its title was confusing (too similar to this one)
Jul
23
revised Understanding the argument that local U(1) leads to coupling of EM and matter
Clarified the question now that I understand the problem a bit better, moved the request for a specific derivation into another question.
Jul
23
asked Show that charge conservation $\partial_\mu J^\mu = 0$ implies global U(1) invariance?
Jul
22
revised Why is particle number conserved, and what are the bounds on non-conservation?
Added a clarification, hope it is now clearer.
Jul
22
comment Why is particle number conserved, and what are the bounds on non-conservation?
@TMS: Completely right, but like I said, I'm not concerned about that kind of non-conservation. That's "trivial", it's what I see every day. What I mean instead: 1) You can identify and count particles. "I see one electron, it leaves a track in a cloud chamber." 2) You can describe the electron as a wavefunction, that gives the probability (amplitide) for finding it somewhere. It will be high in direction of the track. 3) You detect a particle at P. Could it sometimes happen that you also see a particle at Q != P (a duplicate particle, not a reaction product), in violation of QM?
Jul
22
comment Deriving the critical dimension of bosonic string theory
The $-1$ term is gone in the next step ("we thus find..."), and then it's easy to see $D=26$. I'm not sure how he gets there exactly, because the PDF doesn't render correctly for me. But if you collect all the $\alpha_0^{-}$, you can probably get each of the three rows in the next step. Specifically, you can get $\alpha_{-n}^{[i}\alpha_n^{j]}$, which cancels the $-1$. I don't know where some of the $\alpha_0^{-}$ go, or the $p^i, p^j$ come from though. Maybe I'm missing a font, maybe the alphas have a funky commutator :-)
Jul
22
comment Deriving the critical dimension of bosonic string theory
As far as I see, it doesn't vanish, but $f \propto 2nn^2$, so all that remains is $-\sum \frac{4\pi T}{(p^+)^2} \alpha_n^{[i}\alpha_n^{j]}$.
Jul
22
comment Why is particle number conserved, and what are the bounds on non-conservation?
@JohnRennie: Actually I'm fine with the inclusion of QFT. (On the one hand it might make the problem more complicated, on the other hand the solution might be only clear in full QFT.) ... What I meant to say is I'm not interested in particles decaying or splitting or reacting. Of course then the number of particles is not conserved. $e^- \rightarrow e^- e^+ e^-$ in a medium, where the final state electrons have less energy. I'm interested in a failure of wave function collapse (event-by-event, not statistically). This probably implies some non-conservation of charge, energy, etc..
Jul
22
comment Why is particle number conserved, and what are the bounds on non-conservation?
@JohnRennie: Really? I know you can split photons, yielding more with lower energy each, but I'm not talking about that. Rather, place a 500 nm photon in a box, let its wavefunction spread, and see if you sometimes detect two 500 nm photons, or sometimes none.
Jul
22
comment Why is particle number conserved, and what are the bounds on non-conservation?
I'd appreciate suggestions for tags. unitarity is probably not very useful, because people will not search for it. I guess I need one that means "experimental (tests of) QM", and another for "foundations of QM", but I couldn't thinks of a nice tag name.
Jul
22
asked Why is particle number conserved, and what are the bounds on non-conservation?
Jul
22
comment Understanding the argument that local U(1) leads to coupling of EM and matter
@Olaf: Thanks, I forgot that you can put in charge conservation. That also explains where the factors of $e$ come from! ... There are several statements, and we can use some as assumptions, and one as a conclusion. I guess I'm trying to figure out what the most pedagogical or intuitive set of inputs to the argument is.
Jul
22
asked Understanding the argument that local U(1) leads to coupling of EM and matter
Jul
16
revised Lev Landau's “Theoretical Minimum”
Removed [theoretical-physics] again. I still belive it's fitting, but as long as it's only on one question, it's not very useful. Added [education]. Sorry for bumping :-)
Jul
15
reviewed Reject Lev Landau's “Theoretical Minimum”
Jul
15
revised Lev Landau's “Theoretical Minimum”
edited tags
Jul
4
awarded  Custodian
Jul
4
reviewed Reject Lev Landau's “Theoretical Minimum”
Jul
2
accepted Mechanisms of mass generation for Dirac neutrinos