Einstein-Podolsky-Rosen entanglement for self-interacting complex scalar fields

We demonstrate the Einstein-Podolsky-Rosen (EPR) correlations in the Gaussi an trial wavefunctional widely used in the Schrodinger representation of th e self-interacting complex scalar fields (CSF). This demonstration is based on the explicit eigenstates \\xi >, which possess the precise EPR entangle ment and constitute a complete and orthonormal representation, of CSF phi a nd phi (dagger) in the Fock space. To show the entanglement of the Gaussian trial wavefunctional, we evaluate in the < xi\\-representation its 'entang led' Wigner functional resembling the Wigner function of the two-mode squee zed vacuum state, whose quantum entanglement is well known.