No massless boson in chiral symmetry breaking in NJL and Thirring models

Details No massless boson in chiral symmetry breaking in NJL and Thirring models No massless boson in chiral symmetry breaking in NJL and Thirring models

2003-06-10

arxiv.org/abs/hep-th/0306083v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, two figures, Latex

Scientific paper

We show that the chiral symmetry breaking occurs in the vacuum of the massless Nambu-Jona-Lasinio (NJL) and Thirring models without a Goldstone boson. The basic reason of non-existence of the massless boson is due to the fact that the new vacuum after the symmetry breaking acquires nonzero fermion mass which inevitably leads to massive bosons. The new vacuum has a finite condensate of $<\bar \psi \psi>$ with the chiral current conservation. Thus, it contradicts the Goldstone theorem, and we show that the proof of the Goldstone theorem cannot be justified any more for fermion field theory models with regularizations.

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