  Quantum Field Theory (QFT) represents a vast generalization of Quantum
Mechanics (QM), as it deals with systems that have an infinite number of
degrees of freedom. The Stone-von Neumann theorem, which establishes the
equivalence of irreducible representations of the canonical commutation
relations (CCR) in QM, does not extend to QFT. Consequently, QFT admits
multiple inequivalent irreducible representations, leading to a much richer
algebraic structure. This essay aims to explore the physics of QFT from the
operator algebra perspective, particularly focusing on entanglement entropy. We
discuss the role of von Neumann algebras of different types in QFT, describe
the local operator algebra approach to QFT, and explain how entanglement
entropy can be defined in terms of the algebra of observables. Additionally, we
explore the benefits of this approach in concrete applications, specifically in
quantum field theory on curved spacetime.
