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3b. How meaningful are single Feynman diagrams?
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The standard model is a theory defined in terms of a Lagrangian.
To get computable output, Feynman graph techniques are used.
But individual Feynman graphs are meaningless (often infinite);
only the sum of all terms of a given order can be given - after
a process called renormalization - a well-defined (finite) meaning.
This is well-known; so no-one treats the Feynman graphs as real.
What is taken as real is the final outcome of the calculations,
which can be compared with measurements.
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3c. How real are 'virtual particles'?
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All language is only an approximation to reality, which simply is.
But to do science we need to classify the aspects of reality
that appear to have more permanence, and consider them as real.
Nevertheless, all concepts, including 'real' have a fuzziness
about them, unless they are phrased in terms of rigorous mathematical
models (in which case they don't apply to reality itself but only to
a model of reality).
In the informal way I use the notion, 'real' in theoretical physics
means a concept or object that
- is independent of the computational scheme used to
extract information from a theory,
- has a reasonably well-defined and consistent formal basis
- does not give rise to misleading intuition.
This does not give a clear definition of real, of course.
But it makes for example charge distributions, inputs and outputs of
(theoretical models of) scattering experiments, and quarks something
real, while making bare particles and virtual particles artifacts of
perturbation theory.
Quarks must be considered real because one cannot dispense with them
in any coherent explanation of high energy physics.
Virtual particles must not be considered real since they arise only in
a particular approach to high energy physics - perturbation theory
before renormalization - that does not even survive the modifications
needed to remove the infinities. Moreover, the virtual particle content
of a real state depends so much on the details of the computational
scheme (canonical or light front quantization, standard or
renormalization group enhances perturbation theory, etc.) that
calling virtual particles real would produce a very weird picture of
reality.
...
The figurative virtual objects in QFT are there only because of the
well-known limitations of the foundations of QFT. In a nonperturbative
setting they wouldn't occur at all. This can be seen by comparing with
QM. One could also do nonrelativistic QM with virtual objects but
no one does so (except sometimes in motivations for QFT),
because it does not add value to a well-understood theory.
Virtual particles are an artifact of perturbation theory that
give an intuitive (but if taken too far, misleading) interpretation
for Feynman diagrams. More precisely, a virtual photon, say,
is an internal photon line in one of the Feynman diagrams. But there
is nothing real associated with it. Detectable photons are always
real, 'dressed' photons.
Virtual particles, and the Feynman diagrams they appear in,
are just a visual tool of keeping track of the different terms
in a formal expansion of scattering amplitudes into multi-dimensional
integrals involving multiple propaators - the momenta of the virtual
particles represent the integration variables.
They have no meaning at all outside these integrals.
They get out of mathematical existence once one changes the
formula for computing a scattering amplitude.
Therefore virtual particles are essentially analogous to virtual
integers k obtained by computing
log(1-x) = sum_k x^k/k
by expansion into a Taylor series. Since we can compute the
logarithm in many other ways, it is ridiculous to attach to
k any intrinsic meaning. But ...
... in QFT, we have no good ways to compute scattering amplitudes
without at least some form of expansion (unless we only use the
lowest order of some approximation method), which makes
virtual particles look a little more real. But the analogy
to the Taylor series shows that it's best not to look at them
that way. (For a very informal view of QED in terms of clouds of
virtual particles see
http://groups.google.com/groups?sel...@univie.ac.at
and the later mails in this thread.)
A sign of the irreality of virtual particles is the fact that
when one does partial resummations of diagrams (which is essential for
renormalization), many of the virtual particles disappear.
A fully nonperturbative theory would sum everything, and no virtual
particles would be present anymore. Thus virtual particles are
entirely a consequence of looking at QFT in a perturbative way
rather than nonperturbatively.
