Mathematical Theory of Quantum Fields (International Series of Monographs on Physics, 101)

This introduction to the mathematical foundations of quantum field theory is based on operator algebraic methods and emphasizes the link between the mathematical formulations and related physical concepts. The book begins with a general probabilistic description of physics, encompassing both classical and quantum physics, and presents the key physical notions before introducing operator algebraic methods. Operator algebra is then used to develop the theory of special relativity, scattering theory, and sector theory This is an introduction to the mathematical foundations of quantum field theory, using operator algebraic methods and emphasizing the link between the mathematical formulations and related physical concepts. It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context. 1. States And Observables -- 2. Quantum Theory -- 3. The Relativistic Symmetry -- 4. Local Observables -- 5. Scattering Theory -- 6. Sector Theory -- App. A. Hilbert Space And Operators -- App. B. Operator Algebras -- App. C. Free Fields. Huzihiro Araki ; Translated By Ursula Carow-watamura. Includes Bibliographical References (p. [222]-232) And Index.