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Inventiones mathematicae

, Volume 40, Issue 1, pp 59–106 | Cite as

Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics I

  • Sergio Albeverio
  • Raphael Höegh-Krohn
Article

Abstract

We give a theory of oscillatory integrals in infinitely many dimensions which extends, for a class of phase functions, the finite dimensional theory. In particular we extend the method of stationary phase, the theory of Lagrange immersions and the corresponding asymptotic expansions to the infinite dimensional case. A particular application of the theory to the Feyman path integrals defined in previous work by the authors yields asymptotic expansions to all orders of quantum mechanical quantities in powers of Planck's constant.

Keywords

Stationary Phase Quantum Mechanic Asymptotic Expansion Phase Function Dimensional Case 
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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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Sergio Albeverio
    • 1
  • Raphael Höegh-Krohn
    • 1
  1. 1.Institute of MathematicsUniversity of OsloOsloNorway

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