Two-loop quantum corrections to the soliton mass in two-dimensional scalar field theories

Abstract

We study higher-order corrections to the soliton mass in two-dimensional scalar field theories. We show that the second quantum correction (two-loop graphs) to the soliton mass ( M S) is finite provided one orders correctly the non-commuting operators in the effective hamiltonian. That is, the vacuum sector UV counterterm suffices to eliminate the ultraviolet and infinite volume divergences of the one-soliton sector. We evaluate explicitly the finite part of the second quantum correction to M S in the sine-Gordon model. We find that the ratio of the soliton mass to the meson mass is the same in our perturbative calculation, as in the semiclassical one by Dashen, Hasslacher and Neveu, up to two-loop contributions.