Algebraic quantum field theory: objectives, methods, and results

TL;DR

Algebraic quantum field theory offers a comprehensive mathematical framework for relativistic quantum physics, covering all states and providing tools for structural analysis and interpretation.

Contribution

This survey summarizes the objectives, methods, and results of algebraic quantum field theory, emphasizing its operator algebra approach and broad applicability.

Findings

Covers the entire state space including vacuum and thermal states

Provides a foundation for structural and interpretative analysis

Facilitates development of new constructive schemes

Abstract

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. This survey is commissioned by the Encyclopedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo. It is to be published by the Elsevier publishing house.