Re: How real are the "Virtual" partticles?

Eugene Stefanovich wrote: 
Arnold Neumaier wrote:

Eugene Stefanovich wrote:


Arnold Neumaier wrote:



Is Hamiltonian H_0 + H_1 + H_2
expressed in operators a^*, a, c^*, c sufficient to directly obtain
scattering amplitudes by formula (2) or not?

Not _directly_, but via renormalization through LSZ. 

I disagree. One can *directly* insert the Hamiltonian H_0 + H_1 + H_2
in formulas

V = H_1 + H_2
V(t) = exp(-iH_0t) V exp(iH_0t)
S = 1 + i\int V(t) dt - \int V(t) dt \int_{-\infty}{t} V(t') dt' +...(2)

and obtain exact S-operator of renormalized QED (as perturbation series, of course). 

But one still considers only the 1PI diagrams instead of _all_
diagrams (which would be required in the bare theory), and that
constitutes the dressing of vacuum and 1-particle states.


Formula (2) includes all possible diagrams with any number of loops.
It provides all radiative corrections. This is enough for Lamb shifts,
anomalous magnetic moments, etc. However, there is nothing about
dressing in formula (2). All calculations are done with bare particle
states and bare particle creation and annihilation operators.



That's why working with (2) as it is gives wrong formulas.
One needs to restrict the Feynman diagrams obtained from the
bare, meaningless formulas obtained from (2) to those that are 1PI,
and this _is_ the dressing. Except that people usually don't
care about giving it a name. But you can look at Figure 7.8 in
Peskin/Schroeder which is a picture of the dressed state, and relate
it to the computation of the selfenergy which is the renormalization.


Here we disagree. 

We always disagree.

This doesn't make your statements correct, however.
All bare objects in QFT give rise to infinities,
and all dressed objects refer to the renormalized situation.

In fact, 'renormalization' is the common word used nowadays
for what you call 'dressing'. You want to impose upon QFT
your own ideosyncratic view, and simply negate what is there,
because you don't comprehend it.

But it is futile to argue with a blind man about colors...


Arnold Neumaier

.

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