1208.5822 (Shuji Watanabe)

An operator-theoretical treatment of the Maskawa-Nakajima equation in
the massless abelian gluon model    [PDF]

Shuji Watanabe

The Maskawa-Nakajima equation has attracted considerable interest in elementary particle physics. From the viewpoint of operator theory, we study the Maskawa-Nakajima equation in the massless abelian gluon model. On the basis of the Schauder fixed-point theorem, we first show that there is a nonzero solution to the Maskawa-Nakajima equation when the parameter $\lambda$ satisfies $\lambda>2$. Moreover, we show that the solution is infinitely differentiable and strictly decreasing. We thus conclude that the massless abelian gluon model exhibits the spontaneous chiral symmetry breaking when $\lambda>2$. On the basis of the Banach fixed-point theorem, we next show that there is a unique solution 0 to the Maskawa-Nakajima equation when $0<\lambda<1$, from which we conclude that the model realizes the chiral symmetry when $0<\lambda<1$.

View original: http://arxiv.org/abs/1208.5822