**A version of QED without ultraviolet divergences**
Bill Hobba wrote:
Thank you for these references. I briefly looked at them and see that
they offer more than I can swallow. I simply do not understand this
language. It will take me some time to figure out what they are talking
about. If you can show me that EFT or Wilsonian approach can produce
a finite Hamiltonian from which both time evolution and S-matrix
can be calculated using standard quantum-mechanical formulas, I will
shut up. I bet they cannot do that.
I understand much better your third reference
Let me quote from it
" You might still be bothered by many things in the previous section.
When we renormalize physical quantities such as charge and mass, you
might be thinking that these quantities are observable and are not
infinte. So how can you get away with making them divergent and then
ignoring it?! The answer to that question is actually deeper than it
first seems.
First of all, there is a flaw to the skeptic's argument that the
electron is not infinitely massive or carries infinite charge. In fact,
according to QFT, it does! The reason we don't see it is subtle but
beautiful. If the electron has infinite charge, then it has an infinite
amount of energy from the electromagnetic field. This energy manifests
itself by the uncertainty principle which says that the field is allowed
to create and destroy particles in very short times; such particles are
called ``virtual particles''. With this huge amount of energy, the field
is able to produce many particles with charge all around the electron.
But because these virtual particles are charged, they line up with the
field and dampen the strength, analogously to dielectrics in classical
electrodynamics. Hense as you go further away from the electron, its
effective charge becomes weaker due to this dielectric effect, thus
lowering the charge of the electron to the values we measure. "
The infinite "bare" charge is what is present in the mutilated QED
Hamiltonian. The finite "screened" charge is what appears in the
S-matrix as a coefficient in front of scattering amplitudes.
While you are working with S-matrix only you can pretend that everything
is fine and finite. However, when you try to calculate the time
evolution you will face infinite "bare" masses and charges in the
Hamiltonian.
In my approach this infinite Hamiltonian is unitarily transformed
and made finite. This is called "clothing transformation", i.e.,
the transformation from "bare" to "clothed" particles. As a result of
this transformation the "coats" of virtual particles disappear.
These coats are unphysical anyway: nobody have seen these virtual
particles.
Again, I am not questioning successes of QFT in calculating S-matrix
properties. I can easily believe that these successful results can
be achieved in a variety of ways: conventional renormalization,
Wilson's renormalization, EFT, etc. I am claiming that neither of these
approaches is capable of producing a finite Hamiltonian and describe
the time evolution in a consistent fashion.
Eugene. |