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 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 illness of the Goldstone theorem is clarified, and the 'massless boson' expected by way of the theory is digital and corresponds to simply a unfastened massless fermion and antifermion pair.Further, the authors talk about the precise spectrum of the Thirring version by means of the Bethe ansatz options, and the analytical expressions of all of the 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 exhibit that bosons consistently 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 gentle cone vacuum is chargeable for the incorrect prediction of the boson mass.
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Extra resources for Bosons After Symmetry Breaking in Quantum Field Theory
Until now, it is not clarified why the Bogoliubov transformation method can give an exact mass for the Schwinger model. Further, the Bogoliubov transformation method reproduces the right condensate value of the Schwinger model which is obtained analytically. This suggest that the Bogoliubov vacuum state may well be a good vacuum state since the condensate value should exhibit some information of the vacuum structure. 2. Bosonization of Schwinger Model In the Schwinger model, the Coulomb gauge is taken, and in this case, the space part of the vector potential A1 depends on time and corresponds to the zero mode of the boson field .
The induced mass M can be expressed in terms of the cutoff Λ, M= Λ sinh . 29) e− g . Evac = − 2π sinh π g From this value of the vacuum energy, we get to know that the new vacuum 30 Takehisa Fujita, Makoto Hiramoto and Hidenori Takahashi energy is indeed lower than the trivial one. Therefore, the chiral symmetry is broken in the new vacuum state and, effectively, the fermion becomes massive. In the same manner as , we carry out the calculations of the spectrum of the bosons in the Fock space expansion.
3. 55 QED2 with Massive Fermions It should be interesting to make some comments on the boson spectrum in QED 2 with massive fermions. 1) with the fermion mass term 1 4 ¯ µ Dµ − m0 )ψ − Fµν F µν . 24) At the massless limit, there is only one boson which is the Schwinger boson. 25) π where γ denotes Euler’s constant. As the mass increases, the number of the bosonic bound states increases . When the mass is much larger than the coupling constant √gπ , then the system becomes just the same as the nonrelativistic quantum mechanics.
Bosons After Symmetry Breaking in Quantum Field Theory by Takehisa Fujita, Makoto Hiramotoa, Hidenori Takahashi