Talk:B − L

Weak hypercharge

As far as I can see B-L is the same was weak hypercharge. --Michael C. Price ^talk 10:39, 28 October 2008 (UTC)

Seems like it. I say merge the two at weak hypercharge.Headbomb {ταλκ – WP Physics: PotW} 15:16, 28 October 2008 (UTC)

I hesitate only because none of my textbooks make this identification. --Michael C. Price ^talk 16:03, 28 October 2008 (UTC)

Gimme a sec, I got two books here that might give some insight.Headbomb {ταλκ – WP Physics: PotW} 16:16, 28 October 2008 (UTC)

From Griffith's

Building on the parallel with isospin, we are led to consider a weak analog of hypercharge(Y),* which is related to electric charge (Q, in units of e) and the third component of isospin (I³), by the Gell-Mann–Nishijima formula:

$Q=I^{3}+{\frac {1}{2}}Y$

We introduce, then, the "weak hypercharge" current:

$j_{m}^{Y}=2j_{\mu }^{em}-2j_{\mu }^{3}=[Formula.I.don't.want.to.type]$

This is an invariant construct, as far as weak isospin is concerned, for the latter does not touch right-handed components at all [formula i don't want to type]. The underlying symmetry group is called SU(2)_L x U(1). SU(2)_L refers to the weak isospin (with a subscript to remind us that it involves left-handed states only), and U(1) refers to weak hypercharge (involving both chiralities).

Now this is chinese to me, but that might not be to you.Headbomb {ταλκ – WP Physics: PotW} 16:39, 28 October 2008 (UTC)

Also, both articles (B-L and weak hypercharge) say that B-L is an expression of weak hypercharge. I doubt we need to put more thought in the merger than this.Headbomb {ταλκ – WP Physics: PotW} 16:46, 28 October 2008 (UTC)

Okay, let me ask another editor who's worked on it. --Michael C. Price ^talk 19:31, 28 October 2008 (UTC)

Likebox has reservations about the merger. I don't fully understand his reasoning, but think we should defer to it. See his explanation at my talk page. --Michael C. Price ^talk 21:56, 28 October 2008 (UTC)

Then let'S follow his advice. Whenever there's group theory involved, I can't follow a damn thing.Headbomb {ταλκ – WP Physics: PotW} 00:22, 29 October 2008 (UTC)

It's not easy, I'll grant. I good place to start would be at Noether current. --Michael C. Price ^talk 18:16, 29 October 2008 (UTC)

I don't see what that tell me about what in the world is a SU(3)xSU(2)xU(1) group.Headbomb {^ταλκ_{κοντριβς} – WP Physics} 19:54, 29 October 2008 (UTC)

Unfortunately the maths articles are even more poorly written than the physics stuff. But you could try Special unitary group.--Michael C. Price ^talk 05:09, 30 October 2008 (UTC)

PLEASE DON'T MERGE. B-L IS DEFINITELY NOT WEAK HYPERCHARGE, BY ANY MEANS. 147.162.6.125 (talk) 07:29, 7 October 2014 (UTC)

Gauge bosons

The article states that there are gauge bosons associated with B-L called X and Y. This is wrong. GUTs like SU(5) usually have X and Y bosons, but if we just gauge B-L we end up with one neutral gauge boson, in the literature denoted as Z' (Z-prime). The statement about neutrino mass is also questionable; the truth is, if B-L were exact, neutrinos would have to be Dirac particles, which is perfectly fine. Breaking B-L usually leads to Majorana neutrinos, but not always, as it depends on the B-L charge of the scalar field one uses to break the symmetry.

Someone should definitely rewrite the article, if I find the time I will do it in a couple of month. — Preceding unsigned comment added by 133.28.47.102 (talk) 03:29, 13 January 2012 (UTC)

global/gauge U(1) symmetry

It should be clarified which is meant, global or local U(1) symmetry. These are different symmetries. Charge conservation is related to global U(1) symmetry, while gauge invariance is a local U(1) symmetry. Aoosten (talk) 21:18, 22 July 2018 (UTC)

Violated in AdS/CFT

A newly published article claims to prove that B-L is not possible as a symmetry under AdS/CFT:

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.122.191601 — Preceding unsigned comment added by TricksterWolf (talk • contribs) 20:05, 29 June 2019 (UTC)