ISSN:
1432-0916

Source:
Springer Online Journal Archives 1860-2000

Topics:
Mathematics
,
Physics

Notes:
Abstract Some properties of projection operators are investigated by means of a theorem of Borchers. Under the assumptions of (A) spectrum-condition for the energy-operator, (B) locality, (C) uniqueness of an invariant state Ω under time-translations, (D) irreducibility of the global algebra, (E) weak additivity equivalent to the cyclicity of each local ring the following main result is derived: None of two projection operatorsE andF, for which the two equations $$\begin{array}{*{20}c} {[E_t ,F] = 0} & {for} & {\left| t \right|〈 \varepsilon ,} & {and} & {E.F = 0} \\\end{array}$$ are valid, can belong to a local ring. This result includes the following special cases: FromE ∈ ,F ∈ resp. two local rings belonging to the compact regions ℜ1 and ℜ2, ℜ1 spacelike to ℜ2, it follows, thatE. F≠0. ForE a local projection operator andF a projection operator withF=F t identically int (so thatF describes a conserved property) one finds againE. F≠0.

Type of Medium:
Electronic Resource

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