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?
Why do we stress the concept of gauge invariance? The point of a gaugeinvariant theory is that it introduces a symmetry in the calculations, which
makes the theory renormalizable. This means that it is possible, at least in
principle, to make calculations in the form of a perturbation series to all orders
in the coupling constant, that is, for a sum over all possible Feynman diagrams,
including those involving an arbitrary number of exchanged photons.
Bill_K said: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].
Lapidus said: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)?
Parlyne said:There are certainly renormalizable theories which are not gauge theories ([itex]\phi^4[/itex] theories with real [itex]\phi[/itex] 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.