Re: Finite time calculation in QED

On 2005-04-14, Eugene Stefanovich <eugenev@xxxxxxxxxxxx> wrote:
> Igor Khavkine wrote:
>> On 2005-04-12, Eugene Stefanovich <eugenev@xxxxxxxxxxxx> wrote:


> I am interested in interactions of free particles. In fact, I am even
> more interested in the simplest time evolution of one free particle, so
> no localizing potential is needed. I understand that you'll have a
> trouble preparing a single particle state at finite time. That's one
> reason why the RQD approach is better. In this approach, a single localized
> particle at time t=0 is described by the state a^*(x) |0>, where
> x is the vector of position. a^*(x) is a simple Fourier transform of
> usual momentum-space creation operators a^*(p).

I started this thread to show you how to calculate the speed of
propagation of interaction in scalar QED (you claimed to have never seen
on before). For this purpose, calculating explicit expressions for one
particle states is not necessary. Once you learn the general technique,
you can apply it to whatever other problems interest you as well.

>> A free state at t=-oo gets evolved into an eigenstate state of the full
>> Hamiltonian at t=0. That is how the transition will be performed.
>
> Are you saying that the state
>
> exp[iH(0 - -oo)] a^*(p) |0>
>
> is the eigenstate of the Hamiltonian H? Why?
> Is it also an eigenstate of H at t/= 0?

Yes. Replace 0 by any finite t and you'll get the same answer.
Look up the Gellman-Low theorem. I've already given references.
Note that (0 - -oo) is illdefined. You have to take limits to make it
well defined.

>>>If you do not accept the above 3 axioms, then you theory disagrees
>>>with experiment, and has no physical relevance.
>>
>>
>> On the contrary. The model I proposed is based on a simple and
>> justifiable physical assumption. The experimental apparatus is not
>> described by the theory. Without similar assumptions, most of the
>> examples and problems from any text on quantum mechanics have to be
>> thrown out the window as well. If you wish to model the apparatus
>> dynamically within your theory, good luck. At least I don't know how to
>> do it. However, I'm in good company with all the people working on the
>> quantum measurement problem.
>
> Then explain me why non-relativistic quantum mechanics doesn't have
> similar problems. In non-relativistic QM one can easily describe the
> time evolution of
> a single particle (the spreading of the wave packet) without introducing
> any localizing potential and without theoretical modeling of the
> measuring apparatus. All that is needed is the Hamiltonian H and
> formula |Psi(t)> = exp(iHt) |Psi(0)>. The many-particle case is not
> different. I say that the relativistic case is not different either.

You want me to explain why apples are not oranges. That's because they
are different fruit. Usual quantum mechanics corresponds to finitely
many classical degrees of freedom. QFT corresponds to infinitely many
classical degrees of freedom. Relativistic invariance has nothing to do
with it.

If you want to criticise the model I propose please phrase it as a
critique of the ball inside the space ship model. Is the ball
Hamiltonian translation invariant? Is there or not a preferred phrame
for the ball? Can different observers still agree on what's going to
happen to the ball? How?

Igor

.

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