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Letters in Mathematical Physics

, Volume 101, Issue 3, pp 305–322 | Cite as

Removal of UV Cutoff for the Nelson Model with Variable Coefficients

  • Christian Gérard
  • Fumio Hiroshima
  • Annalisa Panati
  • Akito Suzuki
Article

Abstract

We consider the Nelson model with variable coefficients. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. We study the removal of the ultraviolet cutoff.

Mathematis Subject Classification (2010)

81T10 81T20 81Q10 58C40 

Keywords

Nelson model static space-times ground state ultraviolet limit 

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References

  1. 1.
    Ammari Z.: Asymptotic completeness for a renormalized nonrelativistic Hamiltonian in quantum field theory the Nelson model. Math. Phys. Anal. Geom. 3, 217–285 (2000)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bony, J.M.: Caractérisations des opérateurs pseudodifférentiels. Séminaire EDP, Centre de Mathématiques Laurent Schwartz (1996–1997)Google Scholar
  3. 3.
    Derezinski, J., Gérard, C.: Scattering theory of classical and quantum N. Particle Systems. Texts and Monographs in Physics, Springer, Berlin (1997)Google Scholar
  4. 4.
    Gérard C., Hiroshima F., Panati A., Suzuki A.: Infrared divergence of a scalar quantum field model on a pseudo Riemannian manifold. Interdiscip. Inf. Sci. 15, 399–421 (2009)MATHGoogle Scholar
  5. 5.
    Gérard C., Hiroshima F., Panati A., Suzuki A.: Infrared problem for the Nelson model on static space-times. Commun. Math. Phys. 308, 543–566 (2011)ADSMATHCrossRefGoogle Scholar
  6. 6.
    Gérard C., Hiroshima F., Panati A., Suzuki A.: Absence of ground state for the Nelson model on static space-times. J. Funct. Anal. 262, 273–299 (2012)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Nelson E.: Interaction of nonrelativistic particles with a quantized scalar field. J. Math. Phys. 5, 1190–1997 (1964)ADSCrossRefGoogle Scholar
  8. 8.
    Reed M., Simon B.: Methods of Modern Mathematical Physics, vol. 1. Academic Press, New York (1975)Google Scholar

Copyright information

© Springer 2012

Authors and Affiliations

  • Christian Gérard
    • 1
  • Fumio Hiroshima
    • 2
  • Annalisa Panati
    • 3
  • Akito Suzuki
    • 4
  1. 1.Département de MathématiquesUniversité de Paris XIOrsay CedexFrance
  2. 2.Faculty of MathematicsUniversity of KyushuFukuokaJapan
  3. 3.UMR6207 Université Toulon-VarLa Garde CedexFrance
  4. 4.Department of Mathematics, Faculty of EngineeringShinshu UniversityNaganoJapan

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