Dynamical Mass Growing of Fermion with Bare Mass in Two Dimensions

Abstract

We study dynamical mass generation of a fermion with and without a bare mass by coupling with a massive vector field in two-dimensional space-time. To estimate a non-perturbative effect on the fermion mass, we employ the Schwinger-Dyson equations in the lowest-ladder approximation, which are solved by an approximated analytical method and also by a numerical method. We define a purely dynamical mass as a remnant after subtracting the bare mass from a total dynamical mass. We clarify dependence of the purely dynamical mass on the bare mass of the fermion in various region of a coupling constant. Especially we find that the purely dynamical masses growing from the different bare masses coincide with each other at a specific value of the coupling constant where a kind of a duality relation on the bare masses is satisfied.

Comments: This is a posthumous paper submitted with the permission of the author's family, Yoko Matsuyama. K. Nakatsugawa, S. Tanda, and G. E. Volovik examined the manuscript and recognized its scientific value, judging it worthy of archival publication as a contribution to physics. S. Tanda and K. Nakatsugawa further verified its content on behalf of the author to ensure its accuracy