2003/09/18 by Fumio Hiroshima, F. Hiroshima, Hiroshima, F. +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #advanced mathematical theories #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0309044
arxiv created 2003/09/18 · openalex publication_date 2003/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A one-parameter symplectic group \et\dA\t∈\RR derives proper canonical transformations on a Boson Fock space. It has been known that the unitary operator Ut implementing such a proper canonical transformation gives a projective unitary representation of \et\dA\t∈\RR and that Ut can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator \D(\dA) and a phase factor ei∫0t\TA(s)ds with a real-valued function \TA such that Ut=ei∫0t\TA(s)dseit\D(\dA). Key words: Canonical transformations(Bogoliubov transformations), symplectic groups, projective unitary representations, one-parameter unitary groups, infinitesimal self-adjoint generators, local factors, local exponents, normal-ordered quadratic expressions.