# What is a virtual particle?

1. Aug 26, 2014

### JohnPrior3

I understand a virtual particle is not technically a particle, but more of a disturbance in a field. I can't seem to wrap my head around the concept and why it has large implications.

2. Aug 26, 2014

### haushofer

Virtual particles are bookkeeping devices which pop up in QFT due to the superposition principle. See also John Baez' explanation :)

3. Aug 26, 2014

### JohnPrior3

Bear with me, I'm only an undergraduate physics student. I think my biggest area of misunderstanding how they can have negative momentum?

4. Aug 26, 2014

### vanhees71

"Virtual particles" is a quite misleading term of a mathematically well defined object, known as the Feynman propagator in relativistic perturbative quantum field theory. Also the idea that Feynman diagrams depict scattering processes as if you could think about them like collisions of miniature billiard balls is quite misleading. One should keep in mind their quantum (field) theoretical meaning.

They depict in a very clever way formulas that allow you to systematically calculate S-matrix elements for scattering processes in quantum field theory. The external lines depict asymptotic free states of the incoming and outgoing particles, usually plane-wave momentum eigenstates (which are distributions rather than functions by the way). These states can be identified as specific kinds of particles (say electrons) hitting a detector with a quite sharp momentum and can be counted to get measure a cross section for some process of interest (e.g., elastic electron-electron scattering), which is evaluated in QFT using the S-matrix elements which are written cleverly in terms of Feynman diagrams.

The internal lines stand for propagators. These do not symbolized particles that can somehow be detected in the above sense with real-world detectors. They are just mathematical objects used to evaluate the matrix elements.

To really understand elementary particles you have to study quantum field theory and see how the Feynman rules are derived and which meaning the physical quantities have you can define from them. The Feynman diagrams should be seen as a very clever symbolism to write down complicated formulae rather than pictures of what's going on in real-world scattering processes.

5. Aug 26, 2014

### JohnPrior3

Thank you! I definitely need to learn more physics to fully grasp these concepts. I just love the strange phenomena in physics (basically the Standard Model in a nutshell). Hopefully one day I'll be giving explanations like that!

6. Aug 26, 2014

### Demystifier

I often use the following analogy. Suppose you have 1 apple. Then you can write
1 apple = 2 apples + (-1 apple)
But both 2 apples and -1 apple are virtual apples, the only real thing here is 1 apple. The virtual apples are nothing but a computational tool. Does it help?

7. Aug 26, 2014

### JohnPrior3

I understand what you are saying, but could you give me an example of where this would happen?

8. Aug 26, 2014

### Demystifier

Virtual particles are not even a disturbance in a field. They are nothing but a computational tool, not much different from the apples on the right-hand side in the post above.

Last edited: Aug 26, 2014
9. Aug 26, 2014

### Demystifier

See
http://lanl.arxiv.org/pdf/quant-ph/0609163v2.pdf
Sec. 9.3. In particular, references [52,53] are physical examples of using "virtual particles" in CLASSICAL physics.

10. Aug 26, 2014

### tom.stoer

In QFT a "real particle" could be associated with a state in a Hilbert space; technically a "virtual particle" is not a Hilbert space state but an integrated bunch of propagators

11. Aug 26, 2014

### cgk

It may also be helpful to notice that many different kinds of perturbation theories and not-quite-perturbation-theories can be written in terms of diagrams. This is by far not limited to quantum field theory, and I think it would be misguided to say that the diagrams contain any revelations about physical processes.

In some sense, the diagrams in various fields of quantum mechanics are simply depictions of terms which arise from a Wick-theorem-style contraction of creation and destruction operators. Similar diagrams can be obtained even in classical thermal perturbation theories. In all cases, they symbolize terms in expansions of expectation values or matrix elements between operators---nothing more. For example, some people in quantum chemistry use diagrams to compute matrix elements in perturbative and coupled cluster methods (see, for example, Crawford & Schaefer III - An Introduction to Coupled Cluster Theory for Computational Chemists, http://minimafisica.biodec.com/Members/k/Introduction.ps [Broken] for a introduction with little prerequisites). Others do not bother with the diagrams and evaluate the algebraic equations directly. I have yet to see someone who thinks that these kinds of diagrams describe actual physical processes... despite the fact that doing so would be at least as valid as in quantum electrodynamics.

Last edited by a moderator: May 6, 2017
12. Aug 26, 2014

### tom.stoer

These diagrams are artifacts of approximation schemes.

The problem is that usually we do not care about a clear distinction between a) the theory, b) the approximation of the theory and c) the diagrams representing the approximations. So after reading some books or after the first course in QED there's the impression that the theory is identical with the approximation (e.g. perturbation theory in the coupling constant) and that the diagrams (e.g. the Feynman graphs) are identical with the approximation and with the theory itself.

But there are scenarios where these approximations break down, e.g. for non-perturbative regimes, theories which are perturbatively non-renormalizable (but well-defined non-perturbatively), ...

A very simple example is f(z) = 1/(1-z) = 1 + z + z² + z³ + ... You may introduce a graphical representation of the coefficients +1, +1, +1, ... of the series expansion, and you may discuss its physical meaning. Now what about f(z) in a domain where the above expansion becomes invalid? What is the meaning of graphical representation of a series expansion that does not exist?

13. Aug 26, 2014

### vanhees71

Well, it's an open question whether "QED, the full theory" really exists at all. Perturbative QED (of course partially with resummations to tame the soft-photon troubles), however, is a well-defined model, leading to great agreement with high-precision experiments (at least for some quantities like the anomalous magnetic moment of the electron or the Lamb shift of hydrogen atoms).

It is of course true that even the perturbation theory is not mathematically rigorous. Your example with the geometric series is even too optimistic compared with the Dyson series of perturbation theory. While the former is convergent in the disk $|z|<1$, the latter most probably has divergence degree 0.

It is however a good example in the sense of "resummed" perturbation theory. It's most directly related to the Dyson equation. You calculate the self-energy of, say the photon, at some order of perturbation theory and then solve for the Green's function, which schematically is a geometric series of self-energy insertions, but can as well written as the Dyson equation and be directly solved. This leads to an approximation of the full propagator of the interacting theory. There is nothing mysterious concerning the physical meaning of the diagrams, it's just a calculational tool (or just a notation of equations, if you wish) helping you to organize the calculation. You could as well go as Schwinger and never use Feynman diagrams ;-).

14. Aug 26, 2014

### clem

Virtual particles arise as mathematical excitations if 'perturbation theory' is used in a calculation.
They have no physical reality, which is why they are called 'virtual'.
If perturbation theory is not used, there are usually no virtual particles.

15. Aug 26, 2014

### tom.stoer

to cut a long story short
that's it