Local approximations of global Hamiltonian from inclusion of algebras

TL;DR

This paper proposes local approximations to the global Hamiltonian in quantum field theory using algebraic properties, aiding in understanding the structure of conformal field theories.

Contribution

It introduces a method to approximate the global Hamiltonian from local algebraic data, connecting modular Hamiltonians with global dynamics in QFT.

Findings

Global Hamiltonian expressed via modular Hamiltonian of vacuum reduced to a local region

Proposed local Hamiltonians serve as regulators of local algebraic modular Hamiltonians

Method grounded in the operator-algebraic property of nuclearity

Abstract

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 functions of inclusion of algebras and can be viewed as regulators of the modular Hamiltonian of local algebras of QFT