The massless gauge boson had only two degrees of freedom (out of the three of the vector) just as the photon can only be left and right polarized. The great discovery of Peter Higgs was, starting from a gauge theory with massless vertor bosons and adding the symmetry breaking scheme as well as a coupling between the Goldstone scalar and the massless gauge bosons, to find that one can formulate a new theory equivalent to that of a massive vector gauge field. From this particular point consider the direction along the gutter : the massless mode is a a scalar and called the Goldstone boson. The vacuum state picks up one particular point in the gutter, and spontaneously breaks the symmetry of the mexican hat. Yet the true physical degrees of freedom must be constructed from the vacuum state. A particle can roll freely in the gutter, it costs no energy to trigger the movement : that is, this shape exhibits a symmetry corresponding to a massless particle movement.
It is used very often in condensed matter, but its relevance for the generation of mass at a fundamental level is yet to be proven.Ī very short and poor explanation : consider the shape of a mexican hat. In the standard Electroweak model, the Higgs field is responsible for the mass of the force carriers, which are vector bosons. But what about the quarks themselves and the leptons.
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