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  • 1
    Electronic Resource
    Electronic Resource
    On the statistical independence of algebras of observables (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 1318-1328 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We reexamine various notions of statistical independence presently in use in algebraic quantum theory, establishing alternative characterizations for such independence, some of which are also valid without assuming that the observable algebras mutually commute. In addition, in the context which holds in concrete applications to quantum theory, the equivalence of three major notions of statistical independence is proven. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531812
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  • 2
    Electronic Resource
    Electronic Resource
    Bell's inequalities and quantum field theory. II. Bell's inequalities are maximally violated in the vacuum (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2448-2456 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the context of the study of Bell's inequalities carried out in Paper I [J. Math. Phys. 28, 2440 (1987)], it is proven that Bell's inequalities are maximally violated in the vacuum state by suitable spacelike separated observables for both Bose and Fermi free quantum field theories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527734
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  • 3
    Electronic Resource
    Electronic Resource
    Bell's inequalities and quantum field theory. I. General setting (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2440-2447 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Bell's inequalities are briefly presented in the context of order-unit spaces and then studied in some detail in the framework of C*-algebras. The discussion is then specialized to quantum field theory. Maximal Bell correlations β(φ,A(O1), A(O2)) for two subsystems localized in regions O1 and O2 and constituting a system in the state φ are defined, along with the concept of maximal Bell violations. After a study of these ideas in general, properties of these correlations in vacuum states of arbitrary quantum field models are studied. For example, it is shown that in the vacuum state the maximal Bell correlations decay exponentially with the product of the lowest mass and the spacelike separation of O1 and O2. This paper is also preparation for the proof in Paper II [S. J. Summers and R. Werner, J. Math. Phys. 28, 2448 (1987)] that Bell's inequalities are maximally violated in the vacuum state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527733
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  • 4
    Electronic Resource
    Electronic Resource
    Modular inclusion, the Hawking temperature, and quantum field theory in curved spacetime (1996)
    Springer
    Letters in mathematical physics 37 (1996), S. 145-158 
    Details
    ISSN: 1573-0530
    Keywords: 81T05 ; 81T20 ; Hawking temperature ; black-hole spacetimes ; Killing horizon ; modular inclusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A recent result by Borchers connecting geometric modular action, modular inclusion and spectrum condition, is applied in quantum field theory on spacetimes with a bifurcate Killing horizon (these are generalizations of black-hole spacetimes, comprising the familiar black-hole spacetime models). Within this framework, we give sufficient, model-independent conditions ensuring that the temperature of thermal equilibrium quantum states is the Hawking temperature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00416017
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  • 5
    Electronic Resource
    Electronic Resource
    On commutators and self-adjointness (1983)
    Springer
    Letters in mathematical physics 7 (1983), S. 319-326 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract For A a symmetric and H a self-adjoint (not necessarily semi-bounded) operator on a Hilbert space H, we give conditions in terms of the boundedness of operators of the form (H+z)−p (adH)n(A)(H+z) −q , z∈ℂ, n, p, q ∈ ℕ, which imply essential self-adjointness of A on any core of some power of H. By specializing to the case of semibounded H and/or A, we arrive at the same conclusions under weaker conditions. Our results generalize several previous ones of the same nature. Applications to quantum mechanics and quantum field theory are indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420182
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  • 6
    Electronic Resource
    Electronic Resource
    On Bell's inequalities and algebraic invariants (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 321-334 
    Details
    ISSN: 1573-0530
    Keywords: 81T05 ; 46L37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Some algebraic invariants associated with Bell's inequalities are defined for inclusions of von Neumann algebras and studied within the context of general algebraic quantum theory. More special results are proven for quantum field theory which establish that these invariants take infinitely many values. Sharp short-distance bounds on the Bell correlations are also demonstrated in the context of relativistic quantum field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749686
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  • 7
    Electronic Resource
    Electronic Resource
    An Algebraic Characterization of Vacuum States in Minkowski Space. II. Continuity Aspects (1999)
    Springer
    Letters in mathematical physics 49 (1999), S. 337-350 
    Details
    ISSN: 1573-0530
    Keywords: vacuum state ; geometric modular action
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An algebraic characterization of vacuum states in Minkowski space is given which relies on recently proposed conditions of geometric modular action and modular stability for algebras of observables associated with wedge-shaped regions. In contrast to previous work, continuity properties of these algebras are not assumed but derived from their inclusion structure. Moreover, a unique continuous unitary representation of spacetime translations is constructed from these data. Thus, the dynamics of relativistic quantum systems in Minkowski space is encoded in the observables and state and requires no prior assumption about any action of the spacetime symmetry group upon these quantities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007695205044
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  • 8
    Electronic Resource
    Electronic Resource
    An algebraic characterization of vacuum states in Minkowski space (1993)
    Springer
    Communications in mathematical physics 155 (1993), S. 449-458 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An algebraic characterization of vacuum states on nets ofC *-algebras over Minkowski space is given and space-time translations are reconstructed with the help of the modular structures associated with such states. The result suggests that a “condition of geometrical modular action” might hold in quantum field theories on a wider class of spacetime manifolds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096722
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  • 9
    Electronic Resource
    Electronic Resource
    Normal product states for fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model (1982)
    Springer
    Communications in mathematical physics 86 (1982), S. 111-141 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We present sufficient conditions that imply duality for the algebras of local observables in all Abelian sectors of all locally normal, irreducible representations of a field algebra if twisted duality obtains in one of these representations. It is verified that the Yukawa2 model satisfies these conditions, yielding the first proof of duality for the observable algebra in all coherent charge sectors in this model. This paper also constitutes the first verification of the assumptions of the axiomatic study of the structure of superselection sectors by Doplicher, Haag and Roberts in an interacting model with nontrivial sectors. The existence of normal product states for the free Fermi field algebra and, thus, the verification of the “funnel property” for the associated net of local algebras are demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205664
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  • 10
    Electronic Resource
    Electronic Resource
    Nonexistence of quantum fields associated with two-dimensional spacelike planes (1983)
    Springer
    Communications in mathematical physics 89 (1983), S. 221-226 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that in a relativistic quantum field theory satisfying Wightman's axioms, there are no nontrivial field-like operators, or even bilinear forms, associated to a two (or less)-dimensional spacelike plane in Minkowski space. This generalizes Wightman's result that fields can not be defined as operators at a point and stands in contrast to Borchers' result that field operators can be associated with one-dimensional timelike planes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211828
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