# Gauge symmetry and renormalization

1. Nov 15, 2011

### Lapidus

Here and then I read gauge symmetry makes theories renormalizable. Unfortunately I could not find a satisfactory explanation why that so is. Could someone shed some light?

thanks

2. Nov 19, 2011

### Lapidus

It must have something to do with the Ward-Takahashi identities, I believe.

Anybody here who knows a little about gauge symmetry and renormalization and could help?

Note: some texts show how renormalization does not destroy gauge invariance, a fact that at first, of course, is not obvious. But then I read sometimes that gauge symmetry makes renormalization possible, like for example here in Perkins "Particle Astrophysics":

Unfortunately, he fails to explain how exactly gauge symmetry makes theories renormalizable.

thanks again

Last edited: Nov 19, 2011
3. Nov 19, 2011

Well, the base explanation is Noether's Theorem of course. Dunno what exactly explanation you looking for

4. Nov 19, 2011

### Haelfix

Yes, proving this is nontrivial but it was done (and the authors won a Nobel prize for it). The reference is

'T Hooft and Veltman, regularization and renormalization of gauge fields. Nucl. Phys. B44: 189-213, 1972

5. Nov 19, 2011

### Bill_K

A rather good overview of the subject by 't Hooft can be found http://www.staff.science.uu.nl/~hooft101/gthpub/GtH_Yukawa_06.pdf" [Broken].

Last edited by a moderator: May 5, 2017
6. Nov 19, 2011

### Lapidus

Very good overview, indeed.

But as I understand t'Hooft and Veltmann showed that renormalizing a gauge invariant theory does not spoil the gauge invariance of the theory.

My question: is gauge symmetry even necessary to make some theories renormalisable (as it is claimed sometimes)?

Last edited by a moderator: May 5, 2017
7. Nov 19, 2011

### Parlyne

There are certainly renormalizable theories which are not gauge theories ($\phi^4$ theories with real $\phi$ come to mind). What you may be thinking of is that certain types of non-renormalizable theories can be seen to be low-energy effective theories arising from the spontaneous breaking of a gauge symmetry; and, casting them in this light restores renormalizability.

8. Nov 19, 2011

### Lapidus

Well, I was not thinking of much! But I think you correctly sumed up what people mean when they say that gauge symmetry makes some theories renormalizable. Like that Fermi's theory for the weak force is not renormalisable, but the gauge-invariant Weinberg-Salam theory is.

thanks everybody

9. Nov 20, 2011

### aesir

Another reason one usually say that gauge symmetry is required for renormalization is related to the construction of the Standard Model.

In fact if you start from the Yang-Mills Lagrangian and add an arbitrary mass term without the Higgs mechanism, thus spoiling gauge symmetry, you end up with a non renormalizable theory.