Goldstone's theorem in quantum field theory states that in a system with broken continuous symmetry, there may exist excitations with arbitrarily low energy, called the Goldstone bosons.
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Chiral symmetry breaking occurs as before, caused by the same VEV . However, as the spontaneously broken symmetry is now continuous, a massless Goldstone boson appears in the spectrum.
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The properties of these pseudo-Goldstone bosons can normally be thus found by an expansion around the ( exactly ) symmetric theory in terms of the explicit symmetry-breaking parameters.
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From a mathematical perspective the auxiliary field is a variety of Goldstone boson, and its use has advantages when identifying the asymptotic states of the theory, and especially when generalizing beyond QED.
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The controlling approximate symmetries, if they were exact, would be spontaneously broken ( hidden ), and would thus engender massless Nambu-Goldstone bosons, in the absence of explicit breaking.
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Continuing the analogy with QCD, the running gauge coupling ? TC ( ? ) triggers spontaneous chiral symmetry breaking, the technifermions acquire a dynamical mass, and a number of massless Goldstone bosons result.
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Jeffrey Goldstone proved that where symmetry is broken, additional bosons, the Nambu Goldstone bosons, will then be observed in the spectrum of possible states; one canonical example being the phonon in a crystal.
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Using Abelian gauge models, they showed that, " if " such a Goldstone boson is formed, it is " eaten " by the Higgs mechanism, becoming the longitudinal component of the now massive gauge boson.
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In 1973, Weinstein showed that composite Goldstone bosons whose constituent fermions transform in the standard way under " SU " ( 2 ) ?" " U " ( 1 ) generate the weak boson masses
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When N f = 2, i . e ., only the strange quark is also treated as massless, i . e ., 3 } }, all eight pseudoscalar mesons of the quark model become Goldstone bosons.
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