 03388 K. R. Ito and F. Hiroshima
 Local exponents and infinitesimal generators of canonical transformations on Boson Fock spaces
(78K, latex)
Aug 27, 03

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Abstract. A oneparameter 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 normalordered form.
We rigorously derive the selfadjoint operator $\D(\dA)$ and
a phase factor
$e^{i\int_0^t\TA(s)ds}$ with a realvalued function $\TA$
such that
$U_t=e^{i\int_0^t\TA(s)ds}e^{it\D(\dA)}$.
\end{abstract}
{\footnotesize
{\it Key words}: Canonical transformations(Bogoliubov transformations), symplectic groups,
projective unitary representations, oneparameter unitary groups,
infinitesimal selfadjoint generators,
local factors, local exponents,
normalordered quadratic expressions.
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