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Connections in Distributional Bundles and Field Theories

  • D. Canarutto
Conference paper

Abstract

Several standard notions of the differential geometry, such a tangent and jet paces, Frölicher-Nijenhuis bracket, connections and curvature, can be generalized to the case of bundles whose fibres are distribution spaces. Moreover a classical connection on a finite-dimensional bundle yields a connection on an associated distributional bundle. These idea can hed new light on field theories on a curved background.

Keywords

Vector Bundle Dirac Equation Local Expression Curve Background Coordinate Chart 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Schwartz, L. (1966): Théorie des distributions. Hermann, ParisMATHGoogle Scholar
  2. 2.
    Frölicher, A., Kriegl, A. (1988): Linear spaces and differentiation theory. John Wiley & sons, ChichesterMATHGoogle Scholar
  3. 3.
    Kriegl, A., Michor, P. (1997): The convenient setting of global analysis. American Mathematical Society, ProvidenceMATHGoogle Scholar
  4. 4.
    Jadczyk, A., Janyska, J., Modugno, M. (1998): Galilei general relativistic quantum mechanics revisited, in Geometria, Física-Matemática e Outros Ensaios, Homenagem a Antònio Ribeiro Gomes, ed. by A.S. Alves, F.J. Craveiro de Carvalho, J.A. Pereira da Silva, pp. 253–313Google Scholar
  5. 5.
    Modugno, M., Kolář, I. (1998): Ann. Pol. Math. LXVIII, 2Google Scholar
  6. 6.
    Cabras, A., Kolář, A. (1995): Czech. Math. J. 45, 120Google Scholar
  7. 7.
    Canarutto, D.(2000): Archivum Mathematicum Brno 36, 2Google Scholar
  8. 8.
    Canarutto, D., Jadczyk, A., Modugno, M. (1995): Rep. Math. Phys. 36 Google Scholar
  9. 9.
    Canarutto, D. (1998): J. Math. Phys. 39, 9MathSciNetCrossRefGoogle Scholar
  10. 10.
    Canarutto, D.(2000): Acta Appl. Math. 62, 2Google Scholar

Copyright information

© Springer-Verlag Italia 2002

Authors and Affiliations

  • D. Canarutto
    • 1
  1. 1.Dipartimento di Matematica Applicata “G. Sansone”FirenzeItaly

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