By Takehisa Fujita, Makoto Hiramotoa, Hidenori Takahashi

ISBN-10: 1616686588

ISBN-13: 9781616686581

The authors current a unified description of the spontaneous symmetry breaking and its linked bosons in fermion box thought. there is not any Goldstone boson within the fermion box thought types of Nambu-Jona-Lasinio, Thirring and QCD2 after the chiral symmetry is spontaneously damaged within the new vacuum. The disorder of the Goldstone theorem is clarified, and the 'massless boson' anticipated by way of the theory is digital and corresponds to only a loose massless fermion and antifermion pair.Further, the authors speak about the precise spectrum of the Thirring version by means of the Bethe ansatz suggestions, and the analytical expressions of the entire actual observables let the authors to appreciate the essence of the spontaneous symmetry breaking intensive. additionally, the authors study the boson spectrum in QCD2, and convey that bosons continually have a finite mass for SU(Nc) shades. the matter of the sunshine cone prescription in QCD2 is mentioned, and it truly is proven that the trivial mild cone vacuum is accountable for the incorrect prediction of the boson mass.

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19) must vanish. Therefore, we obtain cot 2θn = |ppn | . 21) This Bogoliubov angle θn does not change when the mass varies from m0 to m. In this case, the vacuum is just the same as the trivial vacuum of the massive 26 Takehisa Fujita, Makoto Hiramoto and Hidenori Takahashi case, except that the fermion mass is replaced by the renormalized mass m. The rest of the theory becomes identical to the massive NJL model with the same interaction Hamiltonian H int . Therefore, there is no symmetry breaking, and this vacuum has no condensate.

This is just the same as the spectrum obtained from the Bethe ansatz solutions discussed in the previous section. 9. Bosonization of Massive Thirring Model It is well known that the massive Thirring model is equivalent to the sineGordon field theory [21]. The proof of the equivalence is based on the observation that the arbitrary number of the correlation functions between the two Bethe Ansatz Solutions in Thirring Model 45 models agree with each other if some constants and the fields of the two models are properly identified between them.

Summary of Thirring Model In this section, we have presented a symmetry broken vacuum of the Bethe ansatz solutions in the Thirring model, and have shown that the true vacuum energy is indeed lower than the symmetric vacuum energy. This is quite surprising since the symmetry preserving state often gives the lowest energy state in quantum mechanics. However, in the field theory model, there is also the case in which the symmetry is spontaneously broken in the vacuum state, and this is indeed what is realized and observed in the Thirring model.

### Bosons After Symmetry Breaking in Quantum Field Theory by Takehisa Fujita, Makoto Hiramotoa, Hidenori Takahashi

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