In this article,we study three types of new Yukawa couplings(the boson field is coupled to the fermion field).Two of them are quadratic Yukawa couplings(the boson field is in the form of a vector),and the other one is the matrix Yukawa coupling(the boson field is in the form of a matrix).Based on the above three couplings,we introduce the Higgs mechanism,and find out the properties of the generated mass for the fermions with multiple flavors.For the matrix boson,we introduce its coupling with non-Abelian gauge field.It turns out that the generated mass of the gauge field through the Higgs mechanism is unique.In the large N limit,using the method of auxiliary field,we study the dynamical behaviors of the quadratic Yukawa couplings,including the poles of some dressed propagators.
The Eigenstate Method has been developed to deduce the fermion propagator with a constant external magnetic field. In general, we find its result is equivalent to other methods and this new method is more convenient,especially when one evaluates the contribution from the infinitesimal imaginary term of the fermion propagator. Using the Eigenstate Method we try to discuss whether the infinitesimal imaginary frequency of the fermion propagator in a strong magnetic field and Lorentz-violating extension of the minimal SU（3）×SU（2）×SU（1） Standard Model could have a significant influence on the dynamical mass. When the imaginary term of the fermion propagator in this model is not trivial（√（α-1）eB/3） 〈 σ 〈（√（α-1）2eB/3）, this model gives a correction to the dynamical mass.When one does not consider the influence from the imaginary term（σ 〉√（α-1）2eB/3）, there is another correction from the conventional term. Under both circumstances, chiral symmetry is broken.
The kink structure in the quasiparticle spectrum of electrons in graphene observed at 200 me V below the Fermi level by angle-resolved photoemission spectroscopy（ARPES） was claimed to be caused by a tight-binding electron–phonon（e–ph） coupling in the previous theoretical studies. However, we numerically find that the e–ph coupling effect in this approach is too weak to account for the ARPES data. The former agreement between this approach and the ARPES data is due to an enlargement of the coupling constant by almost four times.
