Using the technique of integration within an ordered product (IWOP) of operators we find some new continuum state vectors which span completeness relations in multi-mode Fock space. This fact tells us that the representation theory in quantum mechanics need to be studied in more detail.
We present the continuous state vector of the total coordinate of multi-particle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product (IWOP) technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.