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Induced Bundles and Nonlinear Wave Equations

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Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 6))

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Abstract

We tell the story of the happy life together of induced bundles, invariant wave equations, and scattering transformations, in the universal cosmos. Also how the first two of these are coming to live together on a more equal footing.

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References

  1. E.P. Wigner, On unitary representations of the inhomogeneous Lorentz group. Ann. Math. (2) 40(1939), 149–204.

    Article  MathSciNet  Google Scholar 

  2. G.W. Mackey, Group representations in Hilbert space. Appendix to Mathematical problems of relativistic physics, I.E. Segal, American Mathematical Society, Providence, 1963, 113–130.

    Google Scholar 

  3. I.E. Segal, Covariant chronogeometry and extreme distances. Astron. & Astrophys. 18(1972), 143–148.

    Google Scholar 

  4. I.E. Segal, H.P. Jakobsen, B. Ørsted, S.M. Paneitz & B. Speh, Covariant chronogemetry, II: Elementary particles. Proc. Natl. Acad. Sci. USA 78(1981), 5261–5265.

    Article  Google Scholar 

  5. I.E. Segal, Covariant chronogeometry and extreme distances, III: Macro-micro relations, lnternatl. J. Theor. Phys. 21(1982), 851–869.

    Article  Google Scholar 

  6. S.M. Paneitz & I.E. Segal, Analysis in space-time bundles, I: General considerations and the scalar bundle. J. Functional Analysis 47(1982), 78–142.

    Article  MathSciNet  MATH  Google Scholar 

  7. S.M. Paneitz & I.E. Segal, Analysis in space-time bundles, II: The spinor and form bundles. J. Functional Analysis 49(1982), 335–414.

    Article  MathSciNet  MATH  Google Scholar 

  8. S.M. Paneitz, Analysis in space-time bundles, III: Higher spin bundles. J. Functional Analysis 54(1983), 18–112.

    Article  MathSciNet  MATH  Google Scholar 

  9. P.D. Lax & R.S. Phillips, Scattering theory, Academic Press, New York, 1967.

    Google Scholar 

  10. G.W. Mackey, Unitary group representations in physics, probability, and number theory, Benjamin/Cummings Co., Reading MA, 1978.

    MATH  Google Scholar 

  11. Y. Choquet-Bruhat, S.M. Paneitz, and I.E. Segal, The Yang-Mills equations on the universal cosmos, J. Functional Analysis 53(1983), 112–150.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Møller, The general theory of relativity, 2nd ed., (1972) Clarendon Press, Oxford, Eng.

    Google Scholar 

  13. B. Kostant, Verma modules and the existence of quasi-invariant differential operators. Non-commutative harmonic analysis (Actes. Colloq., Marseille-Luminy, 1974), 101–128, Lecture Notes in Math. 466, Springer, Berlin, 1975.

    Google Scholar 

  14. H.P. Jakobsen & M. Vergne, Wave and Dirac operators, and representations of the conformal group. J. Functional Analysis 24 (1977), 52–106.

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Speh, Degenerate series representations of the universal covering group of SU(2,2), J. Functional Analysis 33 (1979), 95–118.

    Article  MathSciNet  MATH  Google Scholar 

  16. L. Gross, Norm invariance of mass-zero equations under the conformal group. J. Math. Phys. 5(1964), 687–695.

    Article  MATH  Google Scholar 

  17. B. Ørsted, Conformally invariant differential equations and projective geometry, J. Functional Analysis 44(1981), 1–23.

    Article  MATH  Google Scholar 

  18. K. Jörgens, Uber die nichtlinearen Wellengleichungen der Mathematischen Physik, Math. Ann. 138(159), 179–202.

    Google Scholar 

  19. W.A. Strauss, Decay and asymptotics for □u = F(u), J. Functional Anal. 2(1968), 409–457.

    Article  MATH  Google Scholar 

  20. J.M. Cook, The mathematics of second quantization. Trans. Amer. Math. Soc. 74(1953).

    Google Scholar 

  21. A.S. Wightman & L. Gårding, Fields as operator-valued distributions in relativistic quantum theory. Ark. Fys. 28(1964), 129–184.

    Google Scholar 

  22. I.E. Segal, Nonlinear functions of weak processes. I, J. Functional Analysis 5(1969), 404–456; II, ibid. 6(1970), 91–108.

    Article  Google Scholar 

  23. J.D. Bjorken & S.D. Drell, Relativistic quantum fields, 1965. McGraw-Hill Co., New York.

    MATH  Google Scholar 

  24. N.S. Poulsen, On C∞ vectors and intertwining bilinear forms for representations of Lie groups. J. Functional Analysis 9(1972), 87–120.

    Article  MathSciNet  MATH  Google Scholar 

  25. S.M. Paneitz & I.E. Segal, Self-adjointness of the Fourier expansion of quantized interaction field Lagrangians. Proc. Natl. Acad. Sci. USA 80(1983), 4595–4598.

    Article  MathSciNet  MATH  Google Scholar 

  26. R.S. Phillips. Scattering theory for the wave equations with a short range potential. Indiana Univ. Math. J. 31(1982), 609–639.

    MATH  Google Scholar 

  27. I.E. Segal, Banach algebras and nonlinear semigroups. Integral Equations and Operator Theory 4(1981), 435–455.

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. Irving E. Segal
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California at Berkeley, 94720, Berkeley, CA, USA

    C. C. Moore

  2. Mathematical Sciences Research Institute, 1000 Centennial Drive, 94720, Berkeley, CA, USA

    C. C. Moore

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© 1987 Springer-Verlag New York Inc.

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Segal, I.E. (1987). Induced Bundles and Nonlinear Wave Equations. In: Moore, C.C. (eds) Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics. Mathematical Sciences Research Institute Publications, vol 6. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4722-7_8

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  • DOI: https://doi.org/10.1007/978-1-4612-4722-7_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9130-5

  • Online ISBN: 978-1-4612-4722-7

  • eBook Packages: Springer Book Archive

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