Modular theory for the von Neumann algebras of Local Quantum Physics

Details Modular theory for the von Neumann algebras of Local Quantum Physics Modular theory for the von Neumann algebras of Local Quantum Physics

2008-12-08

arxiv.org/abs/0812.1511v1

Contemp.Math.534:97-120,2011

Mathematics

Operator Algebras

Notes of a course given at the summer school "Aspects of operator algebras and applications", School of Mathematics "Lluis San

Scientific paper

In the first part, the second quantization procedure and the free Bosonic scalar field will be introduced, and the axioms for quantum fields and nets of observable algebras will be discussed. The second part is mainly devoted to an illustration of the Bisognano-Wichmann theorem for Wightman fields and in the algebraic setting, with a discussion on the physical meaning of this result. In the third part some reconstruction theorems based on modular groups will be described, in particular the possibility of constructing an action of the symmetry group of a given theory via modular groups, and the construction of free field algebras via representations of the symmetry group.

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