  We aim at constructing an analog of the Weyl calculus in an infinite
dimensional setting, in which the usual configuration and phase spaces are
ultimately replaced by infinite dimensional measure spaces, the so-called
abstract Wiener spaces. The Hilbert space on which the operators act can be
seen as a Fock space or, equivalently, as a space of square integrable
functions on the configuration space. The construction is not straightforward
and needs to split the configuration space into two factors, of which the first
one is finite dimensional. Then one defines, for a convenient symbol $F$, a
hybrid calculus, acting on the finite dimensional factor as a Weyl operator and
on the other one as an anti-Wick operator, defined thanks to an infinite
dimensional Segal-Bargmann transformation. One can establish bounds on the
hybrid operators. These bounds enable us to prove the convergence of any
sequence of hybrid operators associated with an increasing sequence of finite
dimensional factors. Their common limit is the Weyl operator $OP_h^{weyl}(F)$,
the analog of Calder\'on-Vaillancourt Theorem being a consequence of the upper
mentionned bounds as well.
