Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition
We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on Fock space. Both the bosonic and fermionic case are covered. Conditions for imple...
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1481 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1481 |
| Access Level: | acceso abierto |
| Palabra clave: | Second quantization Bogoliubov transformation Renormalization Many-Body Quantum Mechanics Quantum Field theory Infinite tensor products |
| Sumario: | We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on Fock space. Both the bosonic and fermionic case are covered. Conditions for implementability in the extended sense are stated and proved. From these, we derive conditions for a quadratic Hamiltonian to be diagonalizable by a Bogoliubov transformation that is implementable in the extended sense. Three examples illustrate situations, in which an implementation in the extended sense is possible although the Shale-Stinespring condition fails to hold. |
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