The discussion revolves around the incorporation of isospin freedom into the Dirac equation for protons, particularly regarding the transformation of protons into neutrons. It touches on theoretical frameworks such as effective nucleon theories and quantum chromodynamics (QCD), as well as the implications of non-renormalizability in effective field theories.
Participants express differing views on the implications of non-renormalizability in effective field theories, and there is no consensus on whether effective theories must inherently be non-renormalizable.
The discussion highlights the limitations of effective field theories at high energies and the conditions under which they may still be useful at low energies, but these points remain unresolved.
There were attempts to formulate (effective) nucleon theories, but all these theories turned out to be non-renormalizable. One must use QCD based on quarks and gluons instead. But turning a proton into a neutron (an u- into a d-quark) requires electro-weak theory as only W-bosons change flavours.paweld said:Is it possible to incorporate into Dirac equation for proton
the possibility of its transformation into neutron (isospin freedom)?
I am not so sure about that; non-renormalizability is acceptable (not acceptable) for effective theories (fundamental theories); but uis it necessary the case that effective theories must be non-renormalizable? or let's ask the other way round: what would it mean to have a renormalizable effective theory?DrDu said:Isn't non-renormalisability quasi a charateristic of any effective field theory?