An asymptotically flat ℋ space

The null geodesic equation is solved for the space of Sparling and Tod. Bondi coordinates are found and it is verified that the space construction is idempotent, i.e., the -space of this space is itself, symbolically ² = . Properties of the solution are used to motivate a definition of asymptotic flatness.S.R.C. Postdoctoral Research Fellow.     

Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

Generating fields from data onH − ⋃H +andH − ⋃I +

There are series solutions for characteristic boundary value problems for fields on black hole backgrounds that converge when the data are given on =^{– +}, or on =^{– +}, but may not converge when the data are given on ^{– –}, or on ^{+ +}. We specialize to oscillatory data of frequency and calculate approximate reflection and transmission coefficientsR() andT(), using a field generated by data on =^{– +}, and again, using a field generated by data on ^{– –}. The first calculation gives qualitatively good results at all frequencies at each order of approximation, and quantitatively better results at higher orders of approximation; the second calculation, using the series which may not converge, gives bad results except at very high frequencies. Thus for the physically unnatural case of a field that vanishes on ^– and goes toe ^iv on ⁺ we have a series that is convergent, and uniformly so with respect to frequency, while for the natural case of a field that vanishes on ^– and goes toe ^iv on ^– we are limited to high frequencies. It is argued that a frequency-dependent renormalization of a series of the first type provides an approximation scheme that is convergent, and uniformly so with respect to frequency, for the physically important problems of the second type. The difficulties posed by the -dependent renormalization for the study of incident pulses are discussed.     

Fusion structures from quantum groups: II. Why truncation is necessary

It is shown that a finite, reflection positive, and nontruncated fusion structure on an arbitrary Hopf algebra is trivial in the sense thatq-traces coincide with ordinary traces andq-dimensions coincide with ordinary dimensions. Thus, nontruncated fusion structures are ruled out to describe the fusion rules of quantum field theories with noninteger statistical dimensions and a finite number of superselection sectors.Work supported in part by DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Geometro-stochastic quantization of a theory for extended elementary objects

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of is a resolution kernel Hilbert space constructed in terms of generalized coherent states related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter . The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from .Supported in part by NSERC Research Grant No. A5206.     

A general class of (essentially) iso-spectral perturbations

We consider (essentially) iso-spectral perturbations of operators of the formH _A=A ^* A withA being a densely defined closed linear operator from a Hilbert space to another Hilbert space . We perturbH _A by perturbingA asA+B withB being a linear operator from to . Two classes ofB are defined so as to obtain (essentially) iso-spectral perturbations ofH _A. The abstract results are applied to Schrödinger operators. Our approach gives also a mathematical unification for the so-called factorization method in quantum mechanics.     

Construction of Covariant Differential Calculi on Quantum Homogeneous Spaces

A method of constructing covariant differential calculi on a quantum homogeneous space is devised. The function algebra of the quantum homogeneous space is assumed to be a left coideal of a coquasitriangular Hopf algebra and to contain the coefficients of any matrix over which is the two-sided inverse of one with entries in . The method is based on partial derivatives. For the quantum sphere of Podle and the quantizations of symmetric spaces due to Noumi, Dijkhuizen and Sugitani, the construction produces the subcalculi of the standard bicovariant calculus on the quantum group.     

Some applications of the discrete fourier transform to problems of crystal lattice deformation I

The theory of the discrete Fourier transform [1], [2] is applied in solving a system of difference equations describing the positions of atoms in a deformed crystal lattice. The crystal lattice is approximated by the Born-Kármán model modified to include the internal energy of the undeformed crystal.

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, , , [1] [2]. - , , .

     

Product states for local algebras

Let ()() and () () be the von Neumann algebras associated with the space-tiem regions and respectively in the vacuum representation of the free neutral massive scalar field. For suitably chosen spacelike separated regions and it is proved that there exists a normal product state of (), Some consequences for the algebraic structure of the local rings are pointed out.     

On the characterization of the stationary state of a class of dynamical semigroups

We consider a representation of the entropy production for a completely positive, trace-preserving dynamical semigroup satisfying detailed balance with respect to its faithful stationary state denned on aW*-algebra(): it is expressed as a positive Hermitian form on(), which is analogous to the quantum correlation functions used in the Kubo theory. By considering this Hermitian form as a variation function of a vector in(), an exact characterization of the stationary states of semigroups in a certain class is obtained. On this basis, the problem of characterizing the stationary states discussed by Spohn and Lebowitz for manyreservoir open systems is solved without the restriction to situations near thermal equilibrium.     

Les absorbants de son resonants

Résumé Dans la présente étude, on trouve un bref résumé des travaux de l'auteur, de ses collègues et collaborateurs, concernant l'utilisation des résonateurs dans l'acoustique architecturale. On explique tout d'abord le problème de l'inpluence des résonateurs sur la durée de la réverbération des salles. Se basant sur des considérations théoriques, l'auteur déduit le critère de l'emplacement le plus favorable des matières absorbant le son dans le résonateur même et discute la possibilité de l'absorption totale du son par le résonateur. Dans le cas des systèmes de résonateurs pareils disposés régulièrement sur les murs, le diapason pouvant être obtenu d'une importante absorption est relativement faible. En se servant de systèmes résonants d'absorption comportant plusieurs couches de résonateurs, reliés en série, le diapason de l'absorption importante peut être notablement élargi. L'auteur explique la corrélation du coefficient d'absorption et de l'angle d'incidence de l'onde sonore. En conclusion, on mentionne des exemples de l'utilisation pratique des résonateurs d'absorption les plus simples pour obtenir la caractéristique de l'absorption de fréquence exigée. On discute aussi le problème de l'influence des vibrations simultanées de la paroi extérieure du système de résonance sur la caractéristique de l'absorption du son.

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. . . , , . , , . . ; .

     

Das Verteilungsgesetz der Ferromagnetischen Bereiche vom Standpunkt des Aktivierungsfeldes aus Betrachtet

Zusammenfassung Unter der Voraussetzung, daß das Ahtivierungsfeld für die reversible Bewegung der Blochschen Wände dem Maxwellschen Verteilungsgesetz unterliegt, wird die Entstehung des Maximums der inneren Reibung im Wechselfeld theoretisch erläutert. Weiter wird die Lösung der Differenzialgleichung für die Bewegung einer Blochschen Wand bei gleichzeitiger Wirkung des Wechselfeldes und der Torsionsbeanspruchung gegeben. Die Messung bei einigen Torsionsfrequenzen ermöglicht die Bestimmung gewisser mikroskopischer Konstanten.

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, . . .

     

РАДИАЦИОННЫЙ ЗАХВАТ НЕЙТРОНА ЯДРАМИ Sc,Fe, Cu,Mo, Cd и La

, . 20–1000 keV Sc, Fe, Cu, Mo, Cd La.

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The radiative capture of a neutron on Sc, Fe, Cu, Mo, Cd and La nuclei

The energies and intensities of the transitions of a compound nucleus, produced by the capture of a neutron, were measured by means of a single-crystal scintillation spectrometer. The region of energies 20–1000 keV was measured on Sc, Fe, Cu, Mo, Cd and L a nuclei.

     

A remark on a paper of J. F. Aarnes

LetA be aC*-algebra on the separable Hilbert space , and let be the von Neumann generated byA. LetG be a topological group anda(a) a representation ofG into the group of *-automorphisms ofA. Suppose that each (a) extends to a *-automorphism of , and suppose thata(a)(T)x, y is continuous for eachT inA andx, y and . Then, for a large class of groupsG, one has automatically thata(a)(T)x,y is continuous for allT in andx, y in .Supported in part by NSF Grant GP-9141.     

Maximal violation of Bell's inequalities is generic in quantum field theory

Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space , which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state in there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state . If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state on () given by a density matrix.     

The connection between low-gradient form of the positive column in oxygen and moving striations

The method of sliding photomultipliers was used to study the connection between two forms of the positive column in oxygen — the so-called low-gradientT-form and the highgradientH-form — and the presence of moving striations in the positive column. It was shown that in theT-form of a positive column striations are always present which move from the cathode to anode with a velocity of several thousand metres/sec. The highgradient form of theH-positive column, on the other hand, is not striated. The non-single-valuedness of the value of the longitudinal electric field in a discharge in oxygen is thus explained by the presence or absence of phenomena of a time variable character.

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— - H - — . , - , /. , , . , , , .

     

Quasi-free “second quantization”

Araki and Wyss considered in 1964 a mapAQ(A) of one-particle trace-class observables on a complex Hilbert-space into the fermionC*-algebraU() over . In particular they considered this mapping in a quasi-free representation.We extend the mapAQ(A) in a quasi-free representation labelled byT, 0TI, to allAB()_sa such that tr(T A(1–T)A)< withQ(A) now affiliated with the algebra. This generalizes some well-known results of Cook on the Fock-representationT=0.     

The relativistic polaron without cutoffs

The (non-Lorentz covariant) system consisting of a relativistic scalar Boson field interacting with a single spinless particle (relativistic polaron) with kinetic energy function (m ²+|p|²)^1/2 is studied ind space demensions, whered3. The interaction Hamiltonian is taken to be (x)* (x) (x)dx where has a momentum cutoff. The physical one polaron Hilbert space _ph for this model, corresponding to no cutoff on , is constructed. The total renormalized HamiltonianH without cutoff is constructed as a semibounded self-adjoint operator on _pH . The time zero physical Boson field is also constructed. First order estimates are established for the local (in momentum space) number operators in terms ofH.This research was partially supported by N.S.F. grants GP 28109 and GP 28443 and U.S.A.F. grant AF-AFOSR 743-67.     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .