Is local gauge invariance limiting pQCD to a specific energy regime?

[Cinquero]

Could someone please give me some references or the name of the theory for gauge theories using 'nice' gauge transformations, eg. transformations whose first derivatives in space are bounded?

Why I ask that: my question is if we shouldn't take essential properties of quantum mechanics more serious. If we need high energies to recognize elementary particles as dirac particles, why do we assume them to be dirac particles at low energies? My idea is that analytical properties of the gauge transformations represent the dirac nature of particles (local charge conservation in contrast to global charge conservation). Could it be that this prejudice (of local gauge invariance) limits pQCD to the regime of large Q^2? What happens if we weaken local gauge invariance somewhat?

 

[dextercioby]

I don't see why the gauge transformations for the spinor fields one gets using the Arnowitt-Deser method (so called 'Noether procedure') are not 'nice'.
We don't need high energies to recognize an electron.We have to measure its spin and to test invariance to parity to assess a Dirac field to it.

Daniel.

 

[Cinquero]

I rather thought of the point-like characterization of the electron in space.

 

[dextercioby]

There's no such thing...It is considered a point particle,however,all we can measure is the probability of finding it within a certain finite volume in the real space (or configurations space,if we measure the momentum/energy as well).

Daniel.

 

[Cinquero]

Yes. And in general you need short wavelengths for high resolution... (form factors...)