# Algebraic quantum field theory: objectives, methods, and results

May 22, 2023

Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire state space of a theory is covered, starting from the vacuum over arbitrary configurations of particles to thermal equilibrium and non-equilibrium states. It provides a solid foundation for structural analysis, the physical interpretation of the theory and the development of new constructive schemes.

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This survey is prepared for the second edition of the Encyclopedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo. It is to be published by Elsevier.

Keywords:

Keywords: local quantum physics; local observables; algebraic constructions; vacuum; elementary states; superselection sectors; statistics; thermal states; modular theory; Haag-duality; split property