Comments on: Hidden symmetries

By: Ars Mathematica » Blog Archive » Symmetry Breaking

Ars Mathematica » Blog Archive » Symmetry Breaking — Thu, 03 Nov 2005 05:15:57 +0000

[...] Sean at Cosmic Variance has written a nice introduction to symmetry breaking, one of the oddest (and most successful) ideas in particle physics. [...]

By: Clifford

Clifford — Wed, 26 Oct 2005 18:16:55 +0000

I thought we were agreeing, in fact. I was just trying to point out to the casual, non-technical reader that the arguments made for non-condensation of fermions following from lorentz invariance and the ones made using statistics are not unconnected – in generic dimensions. I was just lending support and trying to connect things with a brief remark…. not disagreeing with anyone….

cheers,

-cvj

By: Moshe

Moshe — Wed, 26 Oct 2005 16:32:50 +0000

Clifford,

Not sure we are agreeing here, my point was that even if you give up on Lorentz invariance (or on spin-statistics, as in low dimensional systems) fermions cannot condense. Basically, in Bose-Einstein condensation most of the particles occupy the same state, the lowest energy one, and fermions cannot do that by their statistics, no matter what their spin happens to be.

By: Ben L

Ben L — Wed, 26 Oct 2005 15:40:17 +0000

Yikes, I’ve been thinking too much about SUSY recently. Of course Anonymous is right.

By: Sean

Sean — Wed, 26 Oct 2005 02:29:01 +0000

Leo — what Ben said, as amended by Anonymous. There just aren’t any scalar fields in the SM that do the job — indeed, we haven’t detected any fundamental scalar fields at all! Quark bilinears can condense, and do break the electroweak symmetry, but the numbers don’t really work out, so we have to invent something new.

Of course, violating Lorentz invariance is possible, and even interesting!

By: Lorentz invariance and you | Cosmic Variance

Lorentz invariance and you | Cosmic Variance — Wed, 26 Oct 2005 02:21:10 +0000

[...] Where were we? Ah yes, spontaneous symmetry breaking. When some field takes on a nonzero value even in empty space, and that field is affected by some symmetry transformation, the resulting symmetry is said to be “spontaneously broken,” and becomes hard for us to see directly. The classic example is the electroweak symmetry of the Standard Model, which is purportedly broken by a Higgs field that we have yet to directly detect. [...]

By: citrine

citrine — Tue, 25 Oct 2005 23:31:29 +0000

On the topic of symmetries in the universe …

http://www.molbio.wisc.edu/facstaff/Carroll.html

By: Anonymous

Anonymous — Tue, 25 Oct 2005 18:54:09 +0000

Take a look at the Hill and Simmons technicolor review, http://arxiv.org/abs/hep-ph/0203079, page 14, if you don’t believe me.

By: Anonymous

Anonymous — Tue, 25 Oct 2005 18:49:11 +0000

Um.

In QCD there are many condensates. Chiral symmetry is broken by a quark condensate, . This breaks electroweak symmetry! The W and Z get a tiny mass in this way.

The observed W and Z masses are much bigger than the QCD scale, though. Hence technicolor, where a techniquark condensate might break electroweak symmetry.

By: Clifford

Clifford — Tue, 25 Oct 2005 17:47:58 +0000

Yes…. and in case people are wondering…these two facts are connected by the spin-statistics theorem.

-cvj