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Abstract
We give a pedagogical introduction to algebraic quantum field theory (AQFT), with the aim of explaining its key structures and features. Topics covered include: algebraic formulations of quantum theory and the GNS representation theorem, the appearance of unitarily inequivalent representations in QFT (exemplified by the van Hove model), the main assumptions of AQFT and simple models thereof, the spectrum condition, ReehSchlieder theorem, split property, the universal type of local algebras, and the theory of superselection sectors. The abstract discussion is illustrated by concrete examples. One of our concerns is to explain various ways in which quantum field theory differs from quantum mechanics, not just in terms of technical detail, but in terms of physical content.
The text is supplemented by exercises and appendices that enlarge on some of the relevant mathematical background. These notes are based on lectures given by CJF for the International Max Planck Research School at the Albert Einstein Institute, Golm (October, 2018) and by KR at the Raman Research Institute, Bangalore (January, 2019).
The text is supplemented by exercises and appendices that enlarge on some of the relevant mathematical background. These notes are based on lectures given by CJF for the International Max Planck Research School at the Albert Einstein Institute, Golm (October, 2018) and by KR at the Raman Research Institute, Bangalore (January, 2019).
Original language  English 

Title of host publication  Progress and Visions in Quantum Theory in View of Gravity 
Subtitle of host publication  Bridging Foundations of Physics and Mathematics 
Editors  Felix Finster, Domenico Giulini, Johannes Kleiner, Jürgen Tolksdorf 
Place of Publication  Cham 
Publisher  Birkhauser 
Number of pages  57 
ISBN (Electronic)  9783030389413 
ISBN (Print)  9783030389406 
Publication status  Published  2020 
Activities
 1 Conference participation

Progress and Visions in Quantum Theory in View of Gravity: Bridging foundations of physics and mathematics
Chris Fewster (Invited speaker)
1 Oct 2018 → 5 Oct 2018Activity: Participating in or organising an event › Conference participation