'Et moi, ... , si j'avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shel.f next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Inhalt

1. Axiomatic Formalism.- 1.1. Introduction. The Algebraic Approach as a Local Quantum Theory.- 1.2. Axioms of the Algebraic Approach.- 1.3. Structure of the Local Quantum Theory: Theorems Derived from the Axioms.- 2. From the Theory of Observables to the Theory of Quantum Fields.- 2.1. Global Theory of Superselection Rules.- 2.2. Local Theory of Superselection Rules: Equivalence Properties of Coherent Sectors.- 2.3. Program for Producing Field Theory by Means of Reconstructing its Charge Sectors.- 3. Field Algebras and their Applications.- 3.1. Op*-Algebras of Field Operators and Vacuum Superselection Rules.- 3.2. Construction and Properties of Von Neumann Field Algebras.- 3.3. Free and Generalized Free Fields.- Appendix. Problems of Constructing Algebraic Gauge Quantum Field Theory.- References.