By Strömberg G.
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Additional info for A Determination of the Solar Motion and the Stream Motion Based on Radial Velocities and Absolute Ma
There, the energy of the new vacuum is lower than that of the free vacuum state, and it breaks the chiral symmetry, but there appears no massless boson. For this claim, however, people may insist that the Bogoliubov transformation does not have to be exact, and therefore there might be some excuse for the symmetry breaking phenomena that occurred in the Thirring model. In this section, we present a new discovery of the symmetry broken vacuum of the Bethe ansatz solution in the Thirring model, and show that the energy of the new vacuum state is indeed lower than that of the symmetric vacuum state even though the symmetric vacuum was considered to be the lowest state in the Thirring model.
24) There is no way to find the corresponding zero mode of the boson field in the massless Thirring model since the axial vector current is always conserved. 5) does not correspond to the massless boson. It is interesting to notice that the problem is closely related to the zero mode which exhibits the infra-red property of the Hamiltonian. This is just consistent with the non-existence of the massless boson due to the infra-red singularity of the propagator in two dimensions . Further, as discussed in the previous section, the Bethe ansatz solutions confirm the finite gap of the massless Thirring spectrum, and this rules out a possibility of any excuse of the massless boson in the massless Thirring model.
Intuitive Discussion Here, we present an intuitive discussion of the chiral symmetry breaking in the NJL models and show that there should not appear any massless boson at all . The treatment here is far from rigorous, but we believe that the essential physics of the spontaneous symmetry breaking phenomena and bosons associated with the symmetry breaking in fermion field theory models should be clarified since there is still a misunderstanding in this problem. The treatment is somewhat similar to the Bogoliubov transformation method which is originally employed by Nambu and Jona-Lasinio when they calculated the vacuum energy after the symmetry breaking in their model.