Local exponents and infinitesimal generators of canonical transformations on Boson Fock spaces

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dc.creatorHiroshima, F.
dc.creatorIto, K. R.
dc.date2003-09-18
dc.date.accessioned2026-07-07T04:30:33Z
dc.date.available2026-07-07T04:30:33Z
dc.descriptionA one-parameter symplectic group $\{e^{t\dA}\}_{t\in\RR}$ derives proper canonical transformations on a Boson Fock space. It has been known that the unitary operator $U_t$ implementing such a proper canonical transformation gives a projective unitary representation of $\{e^{t\dA}\}_{t\in\RR}$ and that $U_t$ can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator $\D(\dA)$ and a phase factor $e^{i\int_0^t\TA(s)ds}$ with a real-valued function $\TA$ such that $U_t=e^{i\int_0^t\TA(s)ds}e^{it\D(\dA)}$. 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.
dc.identifierhttps://arxiv.org/abs/math-ph/0309044
dc.identifierhttp://arxiv.org/abs/math-ph/0309044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57504
dc.subjectMathematical Physics
dc.titleLocal exponents and infinitesimal generators of canonical transformations on Boson Fock spaces
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