Everything in QED is mathematically describable in
terms of Fock states and field operators. If you believe that some
objects in QED deserve the name "virtual", then you should spell out
precisely what they are.

Thus, the statement that a "virtual particle" is not a particle is
formal, true, and has already been given in precise language in this

Until then, the usage of that word remains
informal and any debate as to the reality or measurability of "virtual"
objects or their effects is moot.

"Igor Khavkine" <igor.kh@gmail.com> a crit dans le message de news:
slrneub2si.a7g.igor.kh@corum.multiverse.ca

Everything in QED is mathematically describable in
terms of Fock states and field operators. If you believe that some
objects in QED deserve the name "virtual", then you should spell out
precisely what they are.

Yes, and you should ask that to those who stressed a so-called different
meaning to "virtual", including yourself:
Thus, the statement that a "virtual particle" is not a particle is
formal, true, and has already been given in precise language in this
discussion.

Take a single Feynman diagram in momentum space. Each external leg is
labeled by a 4-momentum, say, p. If p^2 = -m^2, where m is the mass of
the excitation it is associated with, then that particular leg is said
to be "on shell". If this equality does not hold, this leg is said to be
"off shell" OR is said to represent a "virtual particle".
Also, if there is an internal line in the diagram, it is
labelled by a 4-momentum, which generically is not on shell. This
internal line is said to represent "virtual particle exchange".

These are the only places where one encounters the term "virtual
particle" in a non-poetic context. Now you know what I mean by this
term. I, however, am still puzzled by how you use it.

On the other hand. I can take a Fock state, take it to be an eigenstate
of the number operator for some kind of excitation, with eigenvalue,
say, n. Then I can point to this state, say |psi> and call this a "state
with n particles". Then I can ask and answer various questions about
these particles.

Q: What's their total momentum?
A: <psi|P|psi>, where P is the total momentum operator.

Q: What is their total angular momentum?
A: <psi|L|psi>, where L is the angular momentum operator.

Q: What is their charge density distribution?
A: <psi|rho|psi>, where rho is the charge density operator.

Q: What is the probability that these particles will decay into
another set of m particles?
A: |<phi|psi>|^2, where |phi> is the state representing the other
set of m particles.

And so on and so forth. Since there is no state associated with the
objects that get the attribute "virtual", I can't answer any of these
questions for them. Simply put, the "virtual" ones are not particles.

"Igor Khavkine" <igor.kh@gmail.com> a crit dans le message de news:
slrneui0np.4nc.igor.kh@corum.multiverse.ca

Take a single Feynman diagram in momentum space. Each external leg is
labeled by a 4-momentum, say, p. If p^2 = -m^2, where m is the mass of
the excitation it is associated with, then that particular leg is said
to be "on shell". If this equality does not hold, this leg is said to be
"off shell" OR is said to represent a "virtual particle".
Also, if there is an internal line in the diagram, it is
labelled by a 4-momentum, which generically is not on shell. This
internal line is said to represent "virtual particle exchange".

These are the only places where one encounters the term "virtual
particle" in a non-poetic context. Now you know what I mean by this
term. I, however, am still puzzled by how you use it.

It's a mere definition, in a diagram that is but a representation of a
mathematical term, which in turn represents a configuration of fields.
I explained what happen as QED describes it. There is no fundamental
difference, both can be represented by a quantum field, the difference
is the "state" of that field, in relation to its equation of motion.
Various basis can be used to write it, none of them has a priviledged
status. The Fock states and the Feynman diagrams are but one of them.

On the other hand. I can take a Fock state, take it to be an eigenstate
of the number operator for some kind of excitation, with eigenvalue,
say, n. Then I can point to this state, say |psi> and call this a "state
with n particles". Then I can ask and answer various questions about
these particles.

Q: What's their total momentum?
A: <psi|P|psi>, where P is the total momentum operator.

Q: What is their total angular momentum?
A: <psi|L|psi>, where L is the angular momentum operator.

Q: What is their charge density distribution?
A: <psi|rho|psi>, where rho is the charge density operator.

Q: What is the probability that these particles will decay into
another set of m particles?
A: |<phi|psi>|^2, where |phi> is the state representing the other
set of m particles.

And so on and so forth. Since there is no state associated with the
objects that get the attribute "virtual", I can't answer any of these
questions for them. Simply put, the "virtual" ones are not particles.

I really don't see why. If the square of the energy minus square of the
linear momentum isn't zero, the photon is off-shell, then by definition
virtual:
psi|E|psi>^2 - <psi|P|psi>^2 != 0 <=> the photon is off-shell or
virtual. The Feynman diagrams represent the electrons wave function and
the electromagnetic field as well, therefore their is a state for both.

That description is the classical one. With quantum fields, a particles
is still an excitation of a field, whatever the value of the observables
of the field. Mathematically:

A>(x,t) = <Psi(x,t)|A|Psi(x,t)
n(x,t) = <Psi(x,t)|a^+(x,t) a(x,t)|Psi(x,t)

As the Feynman diagrams are for plane waves, the corresponding electron
wave functions fill all the space, and there is a current everywhere so
that the photons are everywhere off-shell. But in real situation, we
have to take a superposition of them. Then, contrary to the diagrams,
there may be a region of space where the current is zero. The
electromagnetic field isn't zero though, and the photons are on-shell
there. All that means that an on-shell photon can be written as a
coherent superposition of off-shell photons! That's the case of a
photon from the sun to earth.

So, that idea of "virtual" particle is unnecessary /enculage de mouche/.

Getting a good insight is a more worthwhile task than nitpicking and
copying out books. Fed up of that discussion. I did my homework, do
yours.

Followup-to: fr.sci.physique

Fock states are vectors in a Hilbert space, Feynman diagrams are not.
How can they be the same?

Ah, and what is the mysterious |psi> that appears in your formulas?

Can you give an explicit example that you will call "virtual"? You use
E>^2 - <P>^2 and not <E^2 - P^2>. I'm sure there is a reason.

Also, I was not aware that Feynman diagrams represent wave functions. How
so?

You probably mean

A(x,t)> = <Psi|A(x,t)|Psi
n(x,t) = <Psi|a^+(x,t) a(x,t)|Psi

Heisenberg states don't have position of time dependence.

Can you write an example of an on-shell photon as a superposition of
off-shell photons? I'm somewhat puzzled by this statement and by much of
the rest of this paragraph.

Different isights for different people. However, I'm still missing
insight into whether you actually use the term "virtual" in a way that
is not merely poetic, and along with it an isight into why this thread
started. If you want to continue, you might want to take advantage of
the Followup-To.