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Multiple representations of extended objects

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 includes bound-state modes and the collective coordinate, while the Matsumoto-Umezawa interaction picture uses the standard massive free field. The asymptotic ground states 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Multiple representations of extended objects

Swanson, Mark S
Physical Review D , Volume 26 (8) – Oct 15, 1982
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1982 The American Physical Society
ISSN
1089-4918
DOI
10.1103/PhysRevD.26.1956
Publisher site
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Abstract

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 includes bound-state modes and the collective coordinate, while the Matsumoto-Umezawa interaction picture uses the standard massive free field. The asymptotic ground states 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.

Journal

Physical Review D – American Physical Society (APS)

Published: Oct 15, 1982

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