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

ABSTRACT.  A 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 
$U_t=e^{i\int_0^t\TA(s)ds}e^{it\D(\dA)}$. 
\end{abstract} 
{\footnotesize 
{\it 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.