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Completeness of wave operators in relativistic quantum mechanics

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Abstract

A combination of geometric and algebraic methods is used to prove asymptotic completeness for Schrödinger-type equations with potential not vanishing at infinity along hyperboloids (in spacetime), and with the free Hamiltonian given by the (not bounded below) relativistic (mass)2 operator. The proof is based on the use of a modified form of local compactness and additional geometric properties of asymptotic scattering states which are needed to distinguish them from states ‘trapped’ inside some hyperboloid for all times.

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References

  1. Enss, V., Comm. Math. Phys. 61, 285–291 (1978); Enss, V., Ann. Phys. (N. Y.) 119, 117–132 (1979); Enss, V., Comm. Math. Phys. 65, 151–165 (1979).

    Google Scholar 

  2. Ruelle, D., Nuovo Cim. 61A, 655–662 (1969).

    Google Scholar 

  3. Mourre, E., Comm. Math. Phys. 68, 91–94 (1979).

    Google Scholar 

  4. Horwitz, L.P. and Piron, C., Helv. Phys. Acta 46, 316 (1973).

    Google Scholar 

  5. Horwitz, L.P. and Soffer, A., Helv. Phys. Acta 53, 112 (1980).

    Google Scholar 

  6. Horwitz, L.P., Lavie, I., and Soffer, A., in ‘Group Theoretical Methods in Physics’, Ann. Israel Phys. Soc. 3, 231 (1980).

    Google Scholar 

  7. Horwitz, L.P. and Lavie, I., Phys. Rev. D15, Nov. (1981).

  8. Simon, B., Ann. Phys. 146, 209–220 (1983).

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    A. Soffer

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  1. A. Soffer
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Supported in part by the Fund for Basic Research administered by the Israeli Academy of Sciences and Humanities Basic Research Foundation.

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Soffer, A. Completeness of wave operators in relativistic quantum mechanics. Lett Math Phys 8, 517–527 (1984). https://doi.org/10.1007/BF00400982

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  • DOI: https://doi.org/10.1007/BF00400982

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