Dirac equation for proton/neutron

[paweld]

Is it possible to incorporate into Dirac equation for proton
the possibility of its transformation into neutron (isospin freedom)?

 

[tom.stoer]

Is it possible to incorporate into Dirac equation for proton
the possibility of its transformation into neutron (isospin freedom)?

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.

 

[DrDu]

Tom,

I was thinking about this question and found this older post.
Isn't non-renormalisability quasi a charateristic of any effective field theory?
Of course we expect divergences when the energy becomes comparable to the binding energy of the quarks, but this does not mean that effective field theories for the proton might not be usefull at low energies.

 

[tom.stoer]

Isn't non-renormalisability quasi a charateristic of any effective field theory?

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?