Local approximations of global Hamiltonian from inclusion of algebras

A bstract We write down the global Hamiltonian of conformal field theory (CFT) in finite volume in terms of the modular Hamiltonian of the vacuum reduced to a local ball-shaped region, and use it to propose local approximations to the global Minkowski Hamiltonian in quantum field theory (QFT). The proposed Hamiltonians are motivated by the operator-algebraic property of nuclearity. They are constructed from the characteristic operators of inclusions of algebras and can be viewed as regulators of the modular Hamiltonian of local algebras of QFT.