On the locality ideal in the algebra of test functions for quantum fields. (English) Zbl 0598.46047

Yngvason, Jakob

Publ. Res. Inst. Math. Sci. 20, 1063-1081 (1984).

Some basic properties of the locality ideal in Borchers’ tensor algebra are established. It is shown that the ideal is a prime ideal and that the corresponding quotient algebra has a faithful Hilbert space representation. A topology is determined for which the positive cone in the quotient algebra is normal, and it is shown that every n-point distribution satisfying the locality condition is a linear combination of positive functionals which also satisfy that condition.

MSC:

46N99	Miscellaneous applications of functional analysis
46F05	Topological linear spaces of test functions, distributions and ultradistributions
46M05	Tensor products in functional analysis
46H10	Ideals and subalgebras
46K10	Representations of topological algebras with involution
81T08	Constructive quantum field theory

Keywords:

locality ideal in Borchers’ tensor algebra; prime ideal; faithful Hilbert space representation; positive functionals

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