  We derive an exact formula for a matrix product state (MPS) representation
(or a PEPS in higher number of dimensions) of the ground state of
translationally invariant bosonic lattice systems in terms of a single
one-dimensional Euclidean quantum mechanical path integral with sources. We
explicitly evaluate the general formula in the special case of the
one-dimensional Klein-Gordon harmonic chain, being a spatial discretization of
1+1 dimensional free boson QFT, obtaining an exact MPS with an infinite
dimensional bond space. We analytically diagonalize the transfer matrix
obtaining two Fock spaces with continuous modes and check that the exact MPS
construction reproduces the correct correlation functions. We also comment on
possible holographic interpretations.
