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  • 1
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give conditions for the existence of field operators on so-called null planes and discuss some consequences of the necessary restriction of the test function space, concerning Haag's theorem and the possibility of unitary mappings intertwining between free fields of different masses. In the last section we discuss conditions under which a unitary representation of the dilatations in the null plane gives rise to a unitary representation of the dilatations in Minkowski space.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper concerns an investigation of the Wilson-Zimmermann (or “short distance”) expansion forA(x)A(y) withx →y whereA(x) is a real scalar field fulfilling Wightman's axioms. If one assumes that such an expansion exists, where the terms of the expansion are operators relatively local toA(x), then the singularities arising in the 4-point-function forx 3 →x 4 must control the singularities of then-point functions (n=4, 5, 6, ...) arising forx j →x x+1,j=1,2,...,n−1. A similar consequence can be drawn if the terms of the expansion are assumed to exist only as bilinear-forms (Section 2). For certain classes of fields one can show that this condition necessary for the short distance expansion is indeed fulfilled (Section 3). The result of the last section is that the above mentioned condition is also sufficient for the Wilson-Zimmermann expansion, interpreted as an expansion into bilinear forms, and also as an operator expansion in a somewhat modified sense.
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  • 3
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A description of relativistic quantum mechanical systems is introduced, in which the states depend on the possible information of the observer. The possibility of information is limited by Einstein-causality for classical systems ( ). Observables belonging to measurements in finite regions of the Minkowskispace have a degenerate spectrum. The measurement of such an observable leads to a mixture; for the description of such a mixture we use a proposal first made byLüders ( ). We assume the locality condition for the observables (ℒ), this means the commutativity of two observables measured in two relatively space-like regions. The main result is the equivalence of (ℒ), ( ), ( ) on the one side and ( ) and ( ) on the other side. ( ) is the Einstein-causality including quantum mechanical systems. The idealisation of a measurement as a point event is used for the derivation of this result.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 13 (1969), S. 216-225 
    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.
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  • 5
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We discuss a recent experiment with interfering neutron beams in the gravitational field of the earth, and show how the explanation of the interference pattern can be obtained by an application of the equivalence principle to the one-particle states. The calculation is carried out in the coordinate system where the gravitational field has been transformed away.
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