Why is electroweak grouped together?

[BWV]

If I understand the standard model correctly (a big assumption)

you have

electromagnetism - U(1) symmetry mediated by the photon
weak interaction - SU(2) symmetry mediated by the W+- & Z bosons
strong interaction - SU(3) symmetry mediated by gluons

is there any reason to view electromagnetism and the weak interaction tied together more than any other combination of the three forces there?

 

[malawi_glenn]

yes there is a good reason -> it works ;-)

See http://arxiv.org/abs/0705.4264 which are very good lecture notes on this topic.

One "can" tie all three forces together in SU(5) (GUT)

The basic observation, which lead one to think about a U(1)xSU(2) unification was that Left and Right handed fermions and antifermions interact different in weak SU(2) interactions (no right handed neutrinos for instance).

 

[blechman]

also, the "U(1)" in the SM gauge group is NOT electromagnetism - it is the "weak hypercharge". so in fact, a better thing to say is:

SU(2) x U(1) == electroweak interactions mediated by W, Z, photon
SU(3) == strong interactions mediated by gluons

When SU(2) x U(1) is spontaneously broken by the Higgs, it breaks to the U(1) electromagnetism which is a COMBINATION of two U(1)'s - the hypercharge and also a subgroup of the SU(2).

 

[malawi_glenn]

All SU(N) groups have a U(1) subgroup, correct me if I am wrong

 

[blechman]

All SU(N) groups have a U(1) subgroup, correct me if I am wrong

i do not correct you. in fact, they have N-1 such subgroups.

 

[nrqed]

i do not correct you. in fact, they have N-1 such subgroups.

Which is equivalent to saying that the rank of SU(N) is N-1 (unless I am mistaken)

 

[blechman]

Which is equivalent to saying that the rank of SU(N) is N-1 (unless I am mistaken)

quite so. each cartan generator generates a U(1) subgroup.