For a physicist, the vacuum is the lowest-energy state, after taking these quantum e

ects into account. This lowest-energy state may not possess all the symmetries of the underlying equations of the physical system, a phenomenon known as 'spontaneous' symmetry breaking, or `hidden' symmetry.

This mechanism of spontaneous symmetry breaking rest came to prominence in the phenomenon of superconductivity, as described in the theory of Bardeen, Cooper and Schrieer. According to this theory, the photon acquires an eective mass when it propagates through certain materials at suciently low temperatures, as discussed earlier by Ginzburg and Landau.

In free space, the massless ness of the photon is guaranteed by Lorentz invariance and U(1) gauge symmetry. A superconductor has a well-dened rest frame, so Lorentz   invariance is broken explicitly. However, the gauge symmetry is still present, though 'hidden' by the condensation of Cooper pairs of electrons in the lowest-energy state (vacuum). It was explicitly shown by Anderson how the interactions with the photon of the Cooper pairs inside a superconductor caused the former to acquire an e

ective mass.

The idea of spontaneous symmetry breaking was introduced into particle physics by Nambu in 1960. He suggested that the small mass and low-energy interactions of pions could be understood as a reection of a spontaneously-broken global chiral symmetry, which would have been exact if the up and down quarks were massless. His suggestion was that light quarks condense in the vacuum, much like the Cooper pairs of superconductivity. When this happens, the `hidden' chiral symmetry causes the pions' masses to vanish, and xes their low-energy couplings to protons, neutrons and each other.

Spontaneous breaking of gauge symmetry was introduced into particle physics in 1964 by Englert and Brout, followed independently by Higgs, and subsequently by Guralnik, Hagen and Kibble. They demonstrated how one could dispose simultaneously of two unwanted massless bosons, a spinless Nambu-Goldstone boson and a gauge boson of an exact local symmetry, by combining them into a single massive vector boson in a fully relativistic theory.

These questions arise that do fermions (also gluon and the weak bosons) acquire mass via Higgs boson? Which field gives mass to Higgs boson?

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