We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A general discussion of the canonical structure of the renormalization group equation is also given.
Abstract Motivated by the construction of continuum tensor networks for interacting field theories, which are relevant in understanding the emergence of space-time in the gauge/gravity correspondence, we derive a non-perturbative functional differential equation for wave functionals in scalar field theories from the exact renormalization group equation. We check the validity of the equation using the perturbation theory. We calculate the wave functional up to the first-order perturbation and verify that it satisfies the equation.
We discuss a two-particle point-irreducible (2PPI) approach to many-body physics which relies on a renormalization group (RG) flow equation for the associated effective action. In particular, the general structure and properties of this RG flow equation are analyzed in detail. Moreover, we discuss how our 2PPI-RG approach relates to density functional theory and argue that it can in principle be used to study ground-state properties of non-relativistic many-body systems from microscopic interactions, such as (heavy) nuclei. For illustration purposes, we use our formalism to compute the ground-state properties of two toy models. Communicated by Achim Schwenk