, Volume 20, Issue 9, pp 957-965

Bogolubov transformations and completeness

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.