Re: How real are the "Virtual" partticles?

From: Eugene Stefanovich (eugenev_at_synopsys.com)
Date: 03/19/05 

Date: Sat, 19 Mar 2005 08:03:19 +0000 (UTC)

Arnold Neumaier wrote:

>
>>contains trilinear terms, like a^+c^+a. This means that if you
>>prepare a state of one electron a^+|0> at time=0, then after a
>>short time, this state will evolve into exp(iHt)a^+|0> which
>>is an infinite linear combination of multiparticle states.
>
>
> Nobody is interested in exp(iHt)a^+|0> since the bare vacuum |0>
> is not a physical state. Nobody is so stupid to try to compute this.

I still haven't got the answer how are you going to describe the
time evolution in QED without using the dressed particle approach.
We both agree that expression exp(iHt)a^+|0> is nonsense.
I know two ways that allow to compute the time evolution.
These two ways are equivalent
(give the same observable predictions).
One way (e.g., Shebeko-Shirokov) is to use the dressed
vacuum |0>_d, dressed
creation-annihilation
operators a^+_d and a_d, and original Hamiltonian with
counterterms H

exp(iHt)a^+_d|0>_d

This is a correct expression, but a^+_d and |0>_d are very complex
combinations of bare particle operators and bare particle states,
respectively. I haven't seen these combinations written down explicitly.

Another way (RQD) is to use dressed particle Hamiltonian H_d and keep
original particle operators and states

exp(iH_dt)a^+|0>

The expression for H_d is not known. There is 2nd order
electron-proton interaction term in my book, and there is a set of
rules how to derive H_d in all orders.

If I understand you correctly, you know a third way to write down
the time evolution of the state vector in QED. I am very interested
to know what it is.
Probably I'll find it in the references you kindly provided in
your other post. Thank you very much.

>
> What is related to measurable quantities are matrix elements
> of a form such as
> <vac|exp(iHt_0) f_1 exp(iHt_1) f_2 exp(iHt_2)|vac>
> where t_0+t_1+t_2 = 0,
> f_1, f_2 are components of physical currents, say,
> and |vac> is the physical vacuum. And these have finite limits.
>

Could you be more specific please. Suppose I would like to find
the time dependence of the expectation value of position (or momentum)
of the electron in the system of two interacting particles
(electron + proton). This quantity is definitely measurable.
How would you do this calculation in QED?
Where are you going to take |vac>, H, f_1, and f_2?

Eugene Stefanovich.

Relevant Pages

  • Re: Finite time calculation in QED
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  • Re: Finite time calculation in QED
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    (sci.physics.research)
  • Re: please help my confusion about particles and irreps.
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