By Takehisa Fujita, Makoto Hiramotoa, Hidenori Takahashi
The authors current a unified description of the spontaneous symmetry breaking and its linked bosons in fermion box conception. there isn't any Goldstone boson within the fermion box concept 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' envisioned by means of the theory is digital and corresponds to simply a loose massless fermion and antifermion pair.Further, the authors talk about the precise spectrum of the Thirring version by way of the Bethe ansatz recommendations, and the analytical expressions of all of the actual observables permit the authors to appreciate the essence of the spontaneous symmetry breaking intensive. additionally, the authors learn the boson spectrum in QCD2, and exhibit that bosons constantly have a finite mass for SU(Nc) colors. the matter of the sunshine cone prescription in QCD2 is mentioned, and it's proven that the trivial mild cone vacuum is answerable for the incorrect prediction of the boson mass.
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Their method and approach are quite different from the present calculation, but both of the calculations agree with each other that there is no massless boson in the NJL model. Here, we should add that there is no serious difficulty of proving the nonexistence of the massless boson from the calculated spectrum. However, if it were to prove the existence of the massless boson, it would have been extremely difficult to do it. For the massless boson, there should be a continuum spectrum, and this continuum spectrum of the massless boson should be differentiated from the continuum spectrum arising from the many body nature of the system.
1p − 1h State Next, we evaluate one particle-one hole (1p − 1h) states. There, we take out one negative energy particle (i0 -th particle) and put it into a positive energy state. 15a) for i = i0 . 15b) is for i = i0 . In this case, the energy of the one particle-one hole states E(i1p1h 0) given as, N = |ki0 | − ∑ |ki |. 15) can be found at the specific value of ni0 and then from this ni0 value on, we find continuous spectrum of the 1 p−1h states. 15) for the lowest 1 p − 1h state. 17c) for ni = −1, −2, · · · , −N0 .
For example, the Thirring model becomes the massive Thirring model where one knows well that there exists one massive boson, and the mass spectrum is obtained as the function of the coupling constant [9, 33, 10]. This means that one cannot find a massless boson in the Hamiltonian of the fermion system. It is also quite important to note that the new Hamiltonian is still described by the same number of the fermion degrees of freedom as the original one. This is in contrast to the boson case where one of the complex field freedom becomes the massless boson ξ.