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arXiv · 2208.03487

Bogoliubov Transformations Beyond Shale-Stinespring: Generic $ v^* v $ for bosons

Sascha Lill
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Abstract

We construct an extension of Fock space and prove that it allows for implementing bosonic Bogoliubov transformations in a certain extended sense. While an implementation in the regular sense on Fock space is only possible if a certain operator $ v^* v $ is trace class (this is the well-known Shale-Stinespring condition), the extended implementation works without any restrictions on this operator. This generalizes a recent result of extended implementability, which required $ v^* v $ to have discrete spectrum.

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Sascha Lill. 2022-08-06. Bogoliubov Transformations Beyond Shale-Stinespring: Generic $ v^* v $ for bosons. https://doi.org/10.1007/978-981-99-5884-9_12

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