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I’ve been thinking about the electroweak phase transition in the early universe, and I have some questions about the form of Coulomb’s law during that epoch.

As I understand it, before the electroweak phase transition, the electromagnetic and weak forces were still united as one force. The Higgs had not yet obtained a non-zero VEV, and the three $W$ particles that correspond to the generators of $SU(2)$, and the $B$ that corresponds to the generator of $U(1)$, were still massless. Here my understanding becomes confused: is it the case that the electroweak force was mediated by all of these particles, i.e. that it was a long range force mediated by four massless gauge bosons? If so, can we derive a classical result that corresponds to something like Coulomb’s law for the electroweak interaction (for e.g. two electrons)? As a very naive guess I could imagine that it looks like Coulomb’s law, but with the electric charge replaced by some combination of the weak isospin and/or hypercharge.

So my questions are:

  1. Is the above picture essentially correct? I would appreciate it if anyone could correct any misconceptions I may have.
  2. What was/were the gauge boson(s) associated with this united electroweak force? The three massless $W’s$, and the $B$?
  3. Can the form of the electroweak interaction during that epoch be derived (‘Coulomb’s law’ at that time) at tree level? If not, can we make an educated guess?
Martin C.
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1 Answers1

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The answer here by Emilio shows how to derive Coulomb's law from Maxwell's equation. There are two questions answered here and here how Coulomb's law comes out of quantum electrodynamics.

So the question is reduced to the before symmetry breaking case, which has all the SU(3)xSU(2)xU(1) symmetries , but where the bosons exchanged have zero mass, and also all the particles in the particle table. Charges though are still there, electrons and quarks etc, it is only the masses that are affected. As masses do not enter in the derivations, linked above, there should be no difference to the attraction or repulsion for the appropriate charges and the corresponding potential, imo.

anna v
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