  The structure of the state-vector space of identical bosons in noncommutative
spaces is investigated. To maintain Bose-Einstein statistics the commutation
relations of phase space variables should simultaneously include
coordinate-coordinate non-commutativity and momentum-momentum
non-commutativity, which lead to noncommutative Fock space. By this we mean
that creation and annihilation operators corresponding to different degrees of
freedom of the bosons do not commute each other. The main character of the
noncommutative Fock space is there are no ordinary number representations
because of the non-commutativity between different number operators. However,
eigenvectors of several pairs of commuting Hermitian operators are obtained
which can also be served as bases in this Fock space. As a simple example, an
explicit form of two-dimensional canonical coherent state in this
noncommutative Fock space is constructed and its properties are discussed.
