In quantum field theory electromagnetic radiation is described by a theory with an abelian gauge symmetry while the weak and strong force are described by theories with non abelian gauge symmetry. We expect observables to be gauge invariant. The field strength tensor in electromagnetism is gauge invariant while that in a yang-mills theory is not. Does this have anything to do with the fact that we can directly observe the electromagnetic radiation like for example using a photon detector while that can't be done with weak or strong force?

I am not interested in the experimental difficulties in doing the same but rather would like to know whether the theory itself rules out direct observation of gluons,W,Z bosons and whether it has to do with the field strength tensor being non gauge invariant.

  • $\begingroup$ It's a long story, but through "the principle of complementarity", the weak observables are, in fact, gauge invariant quantities involving Higgs fields, which, in some gauges, look like the gauge-noninvariant ones... $\endgroup$ – Cosmas Zachos Dec 24 '17 at 0:57

There are different reasons why we cannot directly observe the weak and strong forces, respectively, in the same way that we observe the electromagnetic force.

In the case of the weak force, the gauge-invariance is spontaneously broken beneath the electroweak scale. It is still there but it is `hidden.' One can observe it in experiments that are perform at energy scales above the electroweak scale.

The strong force, which is described by quantum chromodynamics (QCD) is not directly observed because it is confined inside small regions of space inside composite particles. Unfortunately, confinement is not completely understood yet. What we do know is that, as a non-abelian gauge force, it becomes stronger at lower energies. Beneath the QCD scale the force is so strong that it confines itself within composite particles such as the protons. At higher energies the QCD force becomes weaker, a phenomenon called asymptotic freedom. Above the QCD scale it is weak enough to be seen directly in experiments that operate at those energy scales.

So the reason why we don't see these two forces directly in our everyday experience, is not directly related to the gauge properties of the field strength tensor.


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