A few doubts about quantum field theory and high energy physics.

[arroy_0205]

1. I read that the picture of gauge bosons as mediators of interaction originates in and is valid in perturbation theory. But how do we know that picture is correct? We do perturbation theory only because we do not know how to study a system in a fully non-perturbative way. If someday we discover a non-perturbative way of doing all such calculations what will happen to this picture?


2. In quantum electrodynamics a chargeless and massless particle called photon mediates interaction between two electrically charged particles. Then how can such a photon give rise to attraction between oppositely charged particles and repulsion between particles of same charge. I mean how does a chargeless particle cause different effects?

3. Why do we consider 1TeV to be very high energy and difficult to produce while energy of the order of Joule commonplace in daily life?

I hope experts here will bear with my elementary doubts in such difficult subjects.

 

[Accidently]

1. I read that the picture of gauge bosons as mediators of interaction originates in and is valid in perturbation theory. But how do we know that picture is correct? We do perturbation theory only because we do not know how to study a system in a fully non-perturbative way. If someday we discover a non-perturbative way of doing all such calculations what will happen to this picture?


2. In quantum electrodynamics a chargeless and massless particle called photon mediates interaction between two electrically charged particles. Then how can such a photon give rise to attraction between oppositely charged particles and repulsion between particles of same charge. I mean how does a chargeless particle cause different effects?

3. Why do we consider 1TeV to be very high energy and difficult to produce while energy of the order of Joule commonplace in daily life?

I hope experts here will bear with my elementary doubts in such difficult subjects.

1) Actually, we do have non-perturbative method, e.g. lattice QCD
2) The electrical interaction being attractive repulsive is determined by the charge of the charged particle, not photon.
3) Accelerating a proton to 1 TeV means the single proton carried 1TeV energy, whereas 1 Joule energy in a macroscopical object, say a cup of tea, is shared by zillions of proton and electrons, then one particle carried little energy.

 

[jtbell]

1. I read that the picture of gauge bosons as mediators of interaction originates in and is valid in perturbation theory. But how do we know that picture is correct?

We test theories by comparing their predictions with experimental results. In the case of QED for the electromagnetic interaction, I don't know of any experiment that disagrees unambiguously with the theory, outside of experimental uncertainties. Of course, next week someone might make a measurement that goes a few decimal places beyond what has been done before, and thereby uncovers a discrepancy that eventually forces us to modify the theory.

We don't know that QED is "absolutely correct," but I don't see how we can know that any theory is "absolutely correct," given that we can do only a finite number of experiments to test it.

 

[tom.stoer]

1. I read that the picture of gauge bosons as mediators of interaction originates in and is valid in perturbation theory. But how do we know that picture is correct? We do perturbation theory only because we do not know how to study a system in a fully non-perturbative way. If someday we discover a non-perturbative way of doing all such calculations what will happen to this picture?

In order to do that you need some theory (= a collection of mathematical expressions and rules how to use them). Then you can start to test perturbative and non-perturbative approaches. For QCD we have both (applicable in different regimes) and it seems that it works quite well.

As long as we start to write down a Lagrangian which contains gauge bosons we will never find sonmething else and the final theory will always contain gauge bosons; the question whether we do perturbative or non-perturbative calculations is only a technical one.

So the picture with gauge bosons will not break down when we do non-perturbative calculations using gauge bosons; it will break down when we write down something which does not contain gauge bosons ;-)

 

[arroy_0205]

It would be interesting to see if there is an example where a problem can be solved both perturbatively and non-perturbatively and to check if these give same results. Also in case of perturbative calc we should see upto what order the results are same. Perhaps for harmonic oscillator we can do both upto lower order of perturbation but are there more complicated examples?

 

[strangerep]

It would be interesting to see if there is an example where a problem can be solved both perturbatively and non-perturbatively and to check if these give same results. Also in case of perturbative calc we should see up to what order the results are same. Perhaps for harmonic oscillator we can do both up to lower order of perturbation but are there more complicated examples?

Perturbative calculations are notoriously tricky.

Even in classical dynamics, an approach to the quartic anharmonic oscillator by naive perturbation from the harmonic oscillator gives unphysical runaway solutions even at low order. More sophisticated methods are possible, however, in which the various physical parameters (mass, stiffness, etc) are also expanded perturbatively.

Another example is the Morse potential
http://en.wikipedia.org/wiki/Morse_potential
which is useful to describe 2-atom molecules, and for which we have exact nonperturbative solutions. At low energy, the atoms are bound and their relative motion is approximately that of a harmonic oscillator. But as the energy rises, the motion becomes more and more anharmonic until, at a so-called "dissocation threshold" energy, the atoms separate and fly off to infinity. The latter behaviour obviously cannot be accommodated within the sinusoidal solutions of a harmonic oscillator, so here is an example where perturbation breaks down totally for high enough energy, even though it's reasonable for low energy.