Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
Answer
The particles that communicate the Weak interaction, i.e W Bosons and Z bosons are massive. So unlike Electromagnetism which is communicated by massless particles(Photons), the weak interaction has a very short range.
For Massive particles the Potential of interaction falls as
$V(x) = -K \frac{1}{r} e^{-m r} $
The range of this force is approximately equals 1/m.
The strong force is communicated by gluons which as massless, So one can wonder if they have a long ranged interaction like EM. However this effect called colour confinement comes into play. The full explanation of colour confinement is rather technical, and requires a lot study. But roughly speaking, It says that colour charges do not exist in Isolation. If you wish to Separate quark anti quark pairs in mesons, to a distance R one requires an energy proportional to R. So one requires an infinite amount of energy to separate mesons into their constituent quarks. Because all particles that we see, Baryons, mesons and so on are not coloured. Strong force is also a very short ranged force. (a few femto meters as quoted from WIKI). So there are no long ranged classical fields associated with strong and weak forces.
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