General Relativity and Gravitation

, Volume 20, Issue 9, pp 957–965

Bogolubov transformations and completeness

  • Tevian Dray
  • Corinne A. Manogue
Research Articles

DOI: 10.1007/BF00760094

Cite this article as:
Dray, T. & Manogue, C.A. Gen Relat Gravit (1988) 20: 957. doi:10.1007/BF00760094
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Abstract

It is well-known that two complete, orthonormal sets of solutions of the Klein-Gordon equation are related by invertible Bogolubov transformations and that the Bogolubov coefficients therefore satisfy certain identities. We show that the converse is false, namely, that the fact that the Bogolubov coefficients defined by two sets of solutions satisfy these identities doesnot imply that either set can be expanded in terms of the other. Several simple counterexamples are given.

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Tevian Dray
    • 1
    • 2
  • Corinne A. Manogue
    • 1
    • 2
  1. 1.Institute of Mathematical SciencesMadrasIndia
  2. 2.Tata Institute of Fundamental ResearchBombayIndia
  3. 3.Department of MathematicsOregon State UniversityCorvallisUSA
  4. 4.Department of PhysicsOregon State UniversityCorvallisUSA