SCALE SYMMETRY OF QUANTUM SOLITONS

The nonlinear a model Lagrangian for a rotating and vibrating quantum soliton expressed in terms of collective coordinates is shown to possess a symmetry under scale transformation of the chiral field. By utilizing this symmetry, an integro-differential equation determining the chiral angle is obtained. A consistency condition between this equation and the Schrodinger equation for the quantum soliton is discussed, and a relation between the total soliton energy and that related to rotation and vibration is obtained without solving the Schrodinger equation. In the limiting case of only a vibrating or a rotating soliton, the integro-differential equation is reduced to a differential one, and the chiral angle becomes independent of eigensolutions of the relevant Schrodinger equation. The effects of chiral-symmetry breaking due to the pion mass are also examined.