Virtual particles and perturbation theory

[Bobhawke]

I have been told before that virtual particles are just an artefact of perturbation theory, that if we could solve interacting fields exactly we would have no need to talk about virtual particles at all. My question then is if virtual particles are just a mathematical tool to evaluate perturbation series and don't really exist, how do particles actually interact with each other? For example, the electron electron photon vertex is not allowed due to momentum conservation, so how can the electron interact with other charged objects if it cannot emit a photon?

 

[Vanadium 50]

"Vertex" is part of the same formalism you are rejecting when you throw away virtual particles. It's all or nothing - if you want to toss the formalism, you have to toss the whole thing.

 

[hamster143]

Think of particles as localized (but not pointlike) coherent disturbances in the field. Solitary waves, if you like. In a noninteracting field, two disturbances could pass through the same area of space at the same time and be on their ways exactly as they were. If interactions are present, the final state will be nontrivial, old waves will lose some energy, new waves will be created.

 

[K.J.Healey]

I have been told before that virtual particles are just an artefact of perturbation theory, that if we could solve interacting fields exactly we would have no need to talk about virtual particles at all. My question then is if virtual particles are just a mathematical tool to evaluate perturbation series and don't really exist, how do particles actually interact with each other? For example, the electron electron photon vertex is not allowed due to momentum conservation, so how can the electron interact with other charged objects if it cannot emit a photon?

I thought the point of the "virtual particle" was to explain away what you just said. Momentum/energy may not be conserved over a very small distance/time, as smalls the uncertainty principle allows.

 

[fermi]

I have been told before that virtual particles are just an artefact of perturbation theory, that if we could solve interacting fields exactly we would have no need to talk about virtual particles at all. My question then is if virtual particles are just a mathematical tool to evaluate perturbation series and don't really exist, how do particles actually interact with each other? For example, the electron electron photon vertex is not allowed due to momentum conservation, so how can the electron interact with other charged objects if it cannot emit a photon?

You already have received some good answers, but I would add one more because it comes from a somewhat different perspective. I would define a so-called "real" particle to be on-mass-shell. In other words for a real particle p² = m², where p is its four-momentum, and m is its mass (m = 0 is OK.) In contrast, a virtual particle does not satisfy p² = m². In fact for a virtual particle, p² can be anything, it can even be space-like (p² < 0).

For an interacting field theory all particles are virtual. Only when a particle is far away from all other particles, its interactions can be neglected, and it can be said to be on-mass-shell, and it becomes a real particle in that limit only. An extreme example of this involves quarks. You can never separate a quark far away from other quarks. As a result, the quarks are almost always interacting with other quarks nearby and they are almost always off mass shell (except for very brief periods of time, if you can probe them for such short periods (i.e. with deep-inelastic scattering.)) But you don't have to go to such an extreme example. Something easier to understand is the Hydrogen Atom, in which the electron is very slightly off mass shell (by about 1 part in 40000) by the virtue of its binding energy. This electron is virtual (though it is very near to be real.)

In this view then, all interacting particles are virtual, and they become real particles only when the interaction is negligibly weak. This statement has nothing to do with perturbation theory.

 

[Bobhawke]

I think I might understand now. Real particles only exist when they are sufficiently far away from anything that they don't interact, but virtual particles are required to describe interactions. Virtual particles are an artefact of perturbation theory in the sense that we need them to describe interactions, and we usually solve interacting theories using perturbation theory.

Thanks for the replies everyone!

 

[LURCH]

"Vertex" is part of the same formalism you are rejecting when you throw away virtual particles. It's all or nothing - if you want to toss the formalism, you have to toss the whole thing.

Does this also mean throwing out Black Hole evaporation? Or, is there some way to allow for
Hawking radiation without VPPs?

 

[Vanadium 50]

Virtual particles are just a formalism - a calculational tool. While I don't know if there exists a derivation using some other framework, there certainly could be.

 

[yiannis235]

I don't exactly agree with this reply although you have a point.my disagreement is in the example of quarks.yes we can not have them freely moving(at least so far)..however,in feynman diagrams that i assume you know you can calculate processes with quarks being external particles and therefore on shell.of course,you have to combine these cross sections with let's say gluon gluon interactions to have the full proton proton interaction...but quarks can be taken on shell...

 

[Unredeemed]

Think of particles as localized (but not pointlike) coherent disturbances in the field. Solitary waves, if you like. In a noninteracting field, two disturbances could pass through the same area of space at the same time and be on their ways exactly as they were. If interactions are present, the final state will be nontrivial, old waves will lose some energy, new waves will be created.

Would these disturbances be able to explain things like the photoelectric effect where light acts like a particle?

How would they decay into actual matter particles like normal bosons?

 

[Vanadium 50]

my disagreement is in the example of quarks.yes we can not have them freely moving(at least so far).

But you can see bound quarks "orbiting" each other via the energy levels in quarkonium. There is real dynamics there.