2003/06/10 by Makoto Hiramoto, Hiramoto, Makoto, Takehisa Fujita +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0306083
18 pages, two figures, Latex
arxiv created 2003/06/10 · arxiv updated 2009/11/30
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 < ψψ> 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.