  We present a continuous tensor-network construction for the states of quantum
fields called cPEPS (continuous projected entangled pair state), which enjoys
the same spatial and global symmetries of ground-states of relativistic field
theories. We explicitly show how such a state can approximate and eventually
converge to the free field theory vacuum and suggest a
regularization-independent way of estimating the convergence via a universal
term in the fidelity per-site. We also present a detailed bottom-up
construction of the cPEPS as the continuum limit of the conventional lattice
Projected Entangled Pair State (PEPS).
