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net of C-star-systems

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AQFT

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theory (physics), model (physics)

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Idea

The notion of a net C *-systems combines the notion of a C-star system with the notion of local net of observables. In this way, the notion of global gauge groups is introduced into the Haag-Kastler approach to AQFT.

Definition

Let π’œ I be a local net of C-star algebras. Let G be a locally compact topological group and Ξ± G a representation of G on the quasi-local algebra π’œ, that is

π’œ:=clo βˆ₯β‹…βˆ₯(⋃ i∈Iπ’œ i)\mathcal{A} := clo_{\| \cdot \|} \bigl( \bigcup_{i \in I} \mathcal{A}_i \bigr)

so that (π’œ,Ξ± G) is a C-star system.

Definition

The tupel (π’œ I,Ξ± G) is a net of C *-systems if Ξ± g(π’œ i)βŠ†π’œ iβˆ€g∈G.

In the context of Haag-Kastler nets the group G is called the
global gauge group and every automorphism Ξ± g is called a gauge automorphism.

This definition makes sense also if the net consists of star-algebras only, of course.

References

Chapter 6 of:

Revised on May 14, 2012 15:23:11 by Urs Schreiber (82.113.99.198)
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