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Lapidus
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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
thanks
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" .
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.
Gauge symmetry is a fundamental concept in theoretical physics that describes the invariance of a physical theory under certain transformations. In simpler terms, it means that the underlying laws of physics remain unchanged despite certain changes in our perspective or measurement.
Renormalization is a mathematical technique used to remove infinities that arise in theoretical calculations in quantum field theory. It allows us to obtain finite and meaningful results from equations that would otherwise be divergent.
Gauge symmetry is important because it is a fundamental principle underlying many of our theories in physics, such as electromagnetism and the Standard Model of particle physics. It also helps us to understand the underlying symmetries and conservation laws in the universe.
Renormalization helps in theoretical calculations by allowing us to obtain finite and meaningful results from equations that would otherwise be divergent. It also helps to remove unwanted infinities that arise due to the limitations of our current understanding and mathematical tools.
Yes, gauge symmetry and renormalization are universal concepts that can be applied to all physical theories. They are essential for understanding the fundamental laws of nature and have been successfully applied in a wide range of fields, including particle physics, condensed matter physics, and cosmology.