Multiple representations of extended objects

The two methods of quantizing scalar field theories in the soliton sector currently in use in the literature, one developed by Christ and Lee, the other by Matsumoto and Umezawa, are examined simultaneously. It is shown that both may be derived by the same general technique, but correspond to different adiabatic-switching prescriptions. The Christ-Lee switching leads to an interaction picture which included bound-state modes and the collective coordinate, while the Matsumoto-Umezawa interaction picture uses the standard massive free field. The asymptotic ground state in both cases are realized as coherent states, in the Christ-Lee method constructed from the exact classical solution, in the Matsumoto-Umezawa method built around a function which satisfies a simple inhomogeneous equation. It is shown that both representations yield identical results when used to calculate unrenormalized Green's functions. The Lehmann-Symanzik-Zimmermann reduction formulas are developed for both approaches and used to show the two methods predict different results for particle-soliton scattering. Advantages and drawbacks of both approaches are discussed, as well as extensions to multisoliton problems