Functional renormalization group flow of the effective Hamiltonian action

After a brief review of the definition and properties of the quantum effective Hamiltonian action, we describe its renormalization flow by a functional renormalization group equation. This equation can be used for a nonperturbative quantization and study of theories with bare Hamiltonians that are not quadratic in the momenta. As an example, the vacuum energy and gap of quantum mechanical models are computed. Extensions of this framework to quantum field theories are discussed. In particular, one possible Lorentz-covariant approach for simple scalar field theories is developed. Fermionic degrees of freedom, being naturally described by a first order formulation, can easily be accommodated in this approach.