Skip to main content
SpringerLink
Log in

Hermitian structures on solution varieties of nonlinear relativistic wave equations

  • III. Differential Operators on Manifolds
  • Conference paper
  • First Online:
Differential Geometric Methods in Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 905))

  • 527 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ju. L. Daleckii and M.G.Krein, Stability of solutions of differential equations in Banach space, Trans. of Math. Monographs, Vol. 43, 1971.

    Google Scholar 

  2. R. Goodman, “One-sided invariant subspaces and domains of uniqueness for hyperbolic equations,” Proc. Am. Math. Soc. 15, pp. 653–660, 1964.

    Article  MATH  Google Scholar 

  3. E. Jørgensen, “The central limit problem for geodesic random walks,” Zeit. für Wahrscheinlichkeitstheorie, Vol. 32, pp. 1–64, 1975.

    Article  Google Scholar 

  4. C.S. Morawetz and W.A. Strauss, I “Decay and scattering of solutions of a nonlinear relativistic wave equation”, Comm. Pure Appl. Math. Vol. 25, pp. 1–31, 1972; II “On a nonlinear scattering operator,” Comm. Pure Appl. Math. Vol. 26, pp. 47–54, 1973.

    Article  MathSciNet  MATH  Google Scholar 

  5. Reference 1. p. 34

    Google Scholar 

  6. S. Nelson, “L2 asymptotes for the Klein-Gordon equation”, proc. Amer. Math. Soc. Vol. 27, no. 1, pp. 110–116, 1971.

    MathSciNet  MATH  Google Scholar 

  7. S. Paneitz and I. Segal, “Quantization of wave equations and hermitian structures in partial differential varieties,” Proc. Nat. Acad. Sci. USA, in press.

    Google Scholar 

  8. S. Paneitz, “Causal structures in Lie groups and applications to stability of differential equations,” Doctoral dissertation, M.I.T. Dept. of Mathematics, June 1980.

    Google Scholar 

  9. S. Paneitz, “Unitarization of symplectics and stability for causal differential equations in Hilbert space,” J. Func. Anal., in press.

    Google Scholar 

  10. S. Paneitz, “Uniqueness of causal structures in H, unpublished, 1980.

    Google Scholar 

  11. S. Paneitz, “Essential unitarization of symplectic transformations,” unpublished, 1980.

    Google Scholar 

  12. I. Segal, “Foundations of the theory of dynamical systems of infinitely many degrees of freedom, I,” Mat.-fys. Medd. Danske Vid. Selsk. 31, no. 12, 39 pp., 1959.

    Google Scholar 

    Google Scholar 

  13. I. Segal, J. Math. Phys. 1, pp. 468–488.

    Google Scholar 

  14. I. Segal, “Dispersion for nonlinear relativistic equations” I, Proc. Conf. Math. Th. Elem. Part., M.I.T. Press, pp. 79–108, 1966; II, Ann. Scient. de l'Ecole Norm. Sup. (4)1 pp. 459–497, 1968.

    Google Scholar 

  15. I. Segal, “Functional integration and interacting quantum fields,” Proc. Conf. on Func. Int., ed. by A.m.Arthur, 1973.

    Google Scholar 

  16. E. Vinberg, “Invariant convex cones and orderings in Lie groups”, Func. Anal. and Its Appl. Vol. 14, No. 1, pp. 1–13, 1980.

    MathSciNet  MATH  Google Scholar 

  17. M. Weinless, “Existence and uniqueness of the vacuum for linear quantized fields,” J. Func. Anal. 4, pp. 350–379.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, University of California, Berkeley, 94720, Berkeley, California

    Stephen M. Paneitz

Authors
  1. Stephen M. Paneitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Clausthal, 0-3392, Clausthal-Zellerfeld, Germany

    Heinz-Dietrich Doebner  & Stig I. Andersson  & 

  2. Institut für Theoretische Kernphysik, Universität Bonn, Nußallee 14-16, 0-5300, Bonn, Germany

    Herbert Rainer Petry

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Paneitz, S.M. (1982). Hermitian structures on solution varieties of nonlinear relativistic wave equations. In: Doebner, HD., Andersson, S.I., Petry, H.R. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092431

Download citation

  • DOI: https://doi.org/10.1007/BFb0092431

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11197-9

  • Online ISBN: 978-3-540-39002-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation