Which symmetery breaks in SSB?

[moss]

Having read different text on SSB but still I have no clear concept of what or which symmetry breaks in SSB, abelian and non-abelian theory.

What do we mean by term SSB? all I see is the symmetry of ground state is broken but the lagrangian and the given potential is still symmetric under local or global transformation.

Is the complete theory still symmetric? if the ground state is not symmetric?

THANKS.

 

[Orodruin]

SSB is a concept with different realisations. The one you are likely thinking about when posting in this forum is the SSB involved in the Higgs mechanism, where the Higgs vev breaks the electroweak symmetry group SU(2)xU(1) spontaneously.

Yes, the Lagrangian is still symmetric, but the symmetry breaking vacuum provides a symmetry breaking background.

 

[moss]

Thanks for the reply. last week I asked the same thing from a very senior Prof. and his answer was that watch out the english words as its a realization of the ground state. He explained to me something but I did not understand and not to be embarrassed I said that I do understand.

My english is not good so I am still wondering what you mean by ' realization '? and yes I asked over the Higgs mechanism but the same thing is also in Chiral SSB and non-abelian etc.

Is the theory, I mean the lagrangian and EOM and V still symmetric when the concerned field gets a non-zero vev?

 

[ChrisVer]

Well a funny way to read the difference is shown here:
http://philsci-archive.pitt.edu/9295/1/Spontaneous_symmetry_breaking_in_the_Higgs_mechanism.pdf
in the Introduction [the example with the rod]

 

[moss]

THANKS Chris ! in the abstract of the article are the same Qs. I am asking and nobody is addressing the real issue that how just a realization of a ground state can have real physical results. I will certainly read this article tonight.

The term SSB is quite common among physicists but not everybody understand it. Drawing a maxican hat and showing the vev is easy but underlying physics is a tough one IMO.

 

[ChrisVer]

I wouldn't read anything more than the rod example which was meant for a fun answer to your question... in fact I didn't like the abstract. [the site is on the philosophy of science and not scientific]

 

[Orodruin]

The more hands-on example of SSB would be to consider a ferromagnetic material. The energy will be the same regardless of the magnetisation direction, but nature will definitely pick a direction with a measurable magnetisation that is clearly not symmetric as a result.

 

[moss]

Thank you guys, this may be the essay I was looking for. It addresses just the right Qs. e.g how can a symmetry which is not a physical symmetry, produces physical results upon breaking.
The textbooks like Ryder, Peskin, Cheng-Li and Huang are not addressing the Qs. I have therefore this essay is priceless for me.

I knew the Euler Rod example but it also does not address the issue of mass generation while the system is in the same state since its SSB.
I think the author addresses it few pager further up.

Thanks again for the link, you made my day Chris.

 

[Haelfix]

I always liked the following simple analogy. You are sitting at a round table at a polite dinner party. Look to your right there is a glass, look to your left there is a glass. Which one is yours? Everybody at the table is thinking the same thing and is confused, until very suddenly, one person picks up a glass. Then a 'wave' propagates around the table from both sides as people start picking up their now unique glasses.

At the end of the day, you still have the same symmetric configuration, but the particular solution of the problem no longer respects the original symmetry (all glasses are either in the right or left hand). The grown up version of this is the spin chain, and the generalization to QFT is the typical Higgs problem.

 

[moss]

Very nice example. But after the Qs. of symmetry breaking another natural Qs arises that is annoying me for sometime
that ; How can a fake symmetry (gauge symmetry), when broken , generates real masses ? If SSB is just a realization of a system
with no energy input/output then how can it has a physical outcome.

Also if I consider the example of the glasses on the table then Just by picking a glass by someone can produce a real dinner for each seems mind boggling concept.

I am familiar with the mathematics of all these bosonic SSB but mathematics does not points to the underlying subtlety or am I missing something vital?.

 

[Haelfix]

Very nice example. But after the Qs. of symmetry breaking another natural Qs arises that is annoying me for sometime
that ; How can a fake symmetry (gauge symmetry), when broken , generates real masses ?.

Good! This is actually a rather subtle and involved matter that is not universally agreed upon. There is a bit of lore out there called Elitzurs theorem, that states that a local symmetry can never be spontaneously broken in QFT. So what about the Higgs mechanism?? Well, the textbook treatment turns out to be not quite right. What's really happening is that you have to carefully distinguish between a local symmetry, a global symmetry, and an asymptotic symmetry. It turns out that you have to distinguish between the part of a gauge groups that have contractible gauge orbits, and the parts that does not. This latter group (really a quotient group) does not contract to the identity at infinity, and hence contributes to the global symmetries and hence physical charges of a system. It is this part which is spontaneously broken and which directly contributes to a real physical effect, not the purely local part..

I'll see if I can find a reference if I get the chance, there is much more to be said about this.