axiom of choice in Yang-Mills field

[AntonioLao]

In 1954, C. N. Yang and R. L. Mills published a paper in the Physical Review, Volume 96, Number 1 entitled: ‘Conservation of Isotopic Spin and Isotopic Gauge Invariance’. This paper explained the near physical symmetry between nucleons. These are the proton and the neutron. Principle of local symmetry requires the distinction between proton and neutron to be arbitrary from point to point. However, the axiom of choice limits this arbitrariness to one local space-time point such that once we choose a proton and a neutron at a point; we are then not free to make any choices at other space-time points. Nevertheless, the principle of isotopic gauge invariance allows this arbitrariness to exist if and only if the electromagnetic field effect is neglected.

[Guille]

What if the electromagnetic field effect is NOT neglected? Does it not exist then? or jsut it exists in smaller quantity?

[AntonioLao]

What if the electromagnetic field effect is NOT neglected?

I need to look up something before I have a reply for your question.

[AntonioLao]

What if the electromagnetic field effect is NOT neglected?

Then the isopin axis of the proton and neutron is distinctive for each of them. The proton becomes positively charged and the neutron's mass increases slightly. The free neutron dies in about 12 minutes, while the free proton lives forever more than [math]10^{33}[/math] years.