Abstract
In this chapter, we discuss the scattering theory of Lax and Phillips (Lax and Phillips 1967), originally developed for the description of resonances in the scattering of classical waves, such as electromagentic or acoustic waves, off compactly supported obstacles. In Appendix B, we give an extensive treatment of the mathematical background enabling a more complete understanding of the mathematical structure underlying a theory of this type, which seems to be categorical for the description of resonances.
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Notes
- 1.
The 5D gauge covariant extensions of the Maxwell theory (Saad 1989; Aharonovich and Horwitz 2010; Wesson 2006) contains dynamical evolution of the radiation fields, as in the original Lax and Phillips (1967) work.
- 2.
See Strauss and Horwitz (Strauss 2000b) for a detailed discussion of the \((N,\theta , V)\) particle content of the resonances. We furthermore remark that the estimates of the values of the complex poles are not very different from those that follow from those of the model used by Wu and Yang (1964).
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Horwitz, L., Strauss, Y. (2020). Semigroups and Lax Phillips Theory. In: Unstable Systems. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-030-31570-2_2
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DOI: https://doi.org/10.1007/978-3-030-31570-2_2
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