Bogolubov transformations and completeness
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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.
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