Decomposable operators application to K.M.S. weights in a decomposable von Neumann algebra

Jurzak, J. P.

doi:10.1016/0034-4877(75)90064-6

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…The isotony in ν-almost every sector was established in Theorem 3.4. From [24,Prop. II.2] it follows that for a fixed W 0 ∈ W, Ω 0 (ζ) is cyclic and separating for R(W 0 )(ζ) for ν-almost all ζ.…”

Section: Conditions (A)-(c) Hold In ν-Almost All Sectorsmentioning

confidence: 99%

“…As already mentioned, the factorial components R(ζ) in the central decomposition of R indeed act irreducibly on the respective subspaces H(ζ) since Z = R ′ by Proposition 2.1. The representation U(P ↑ + ) of the identity component of the Poincaré group and the subspace E 0 H are decomposed in [19], and the attendant assertions made above are proven there, using results in [24]. Although the net {R(W )} W ∈W was also decomposed in [19], there the argument was framed for locally generated nets for which C is the set of double cones; a concrete choice of a countable "dense" subcollection of double cone algebras was given there.…”

Section: Invariance and Decompositionmentioning

confidence: 99%

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Geometric Modular Action and Spontaneous Symmetry Breaking

Buchholz

Summers

2005

Ann. Henri Poincaré

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We study spontaneous symmetry breaking for field algebras on Minkowski space in the presence of a condition of geometric modular action (CGMA) proposed earlier as a selection criterion for vacuum states on general space-times. We show that any internal symmetry group must commute with the representation of the Poincaré group (whose existence is assured by the CGMA) and each translationinvariant vector is also Poincaré invariant. The subspace of these vectors can be centrally decomposed into pure invariant states and the CGMA holds in the resulting sectors. As positivity of the energy is not assumed, similar results may be expected to hold for other space-times.

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Section: Conditions (A)-(c) Hold In ν-Almost All Sectorsmentioning

confidence: 99%

Section: Invariance and Decompositionmentioning

confidence: 99%