Types of von Neumann algebras associated with extremal invariant states

A globalized version of the following is proved. Let be a factor acting on a Hilbert space ,G a group of unitary operators on inducing automorphisms of ,x a vector separating and cyclic for which is up to a scalar multiple the unique vector invariant under the unitaries inG. Then either is of type III or _x is a trace of . The theorem is then applied to study the representations due to invariant factors state of asymptotically abelianC*-algebras, and to show that in quantum field theory certain regions in the Minkowski space give type III factors.     

Global properties of radial wave functions in Schwarzschild's space-time

Two solutions ₅(x, x _s) and ₆(x, x _s) related to the irregular singular point atx=+ of the radial wave equation in Schwarzschild's space-time are studied as functions of the independent variablex and the parameterx _s. Analytic continuations of ₅ and ₆ are derived and their relation to the flat-space case solutions is established. Explicit expressions for ₃(x, x _s) and ₄(x, x _s) (the solutions about the regular singular point atx=x _s) are given. From these expressions and the analytic continuations of ₅ and ₆ the coefficients relating linearly ₅ and ₆ with _i (i=1, 2, 3, 4) are calculated.     

Remarks on the modular operator and local observables

In this paper we give a characterization of the modular group of a von Neumann algebra , with a cyclic and separating vector, which provides at the same time a necessary and sufficient condition so that two von Neumann algebras ₁ and ₂, such that ₁₂, are the mutual commutants, i.e. ₁=₂.An application is made to the duality property in Quantum Field Theory, and we give a sufficient condition for PCT invariance in a theory of local observables.Partially supported by C.N.R.     

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.     

The significance of conformal inversion in quantum field theory

The 2-point functions of Euclidean conformal invariant quantum field theory are looked at as intertwining kernels of the conformal group. In this analysis a fundamental role is played by a two-element groupW, whose non-identity element =R·I consists of the conformal inversionR multiplied by a space-time reflectionI. The propagators of conformal invariant quantum field theory are determined by the requirement of -covariance. The importance of the -inversion in the theory of Zeta-functions is mentioned.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

HeiddenSL(n) symmetry in conformal field theories

We prove that an irreducible representation of the Virasoro algebra can be extracted from an irreducible representation space of theSL(2, ) current algebra by putting a constraint on the latter using the Becchi-Rouet-Stora-Tyutin formalism. Thus there is aSL(2, ) symmetry in the Virasoro algebra, but it is gauged and hidden. This construction of the Virasoro algebra is the quantum analogue of the Hamiltonian reduction. We then are naturally lead to consider a constrainedSL(2, ) Wess-Zumino-Witten model. This system is also related to quantum field theory of coadjoint orbit of the Virasoro group. Based on this result, we present a canonical derivation of theSL(2, ) current algebra in Polyakov's theory of two-dimensional gravity; it is a manifestation of theSL(2, ) symmetry in conformal field theory hidden by the quantum Hamiltonian reduction. We also discuss the quantum Hamiltonian reduction of theSL(2, ) current algebra and its relation to theW _n -algebra of Zamolodchikov. This makes it possible to define a natural generalization of the geometric action for theW _n -algebra despite its non-Lie-algebraic nature.This paper is dedicated to the memory of Vadik G. Knizhnik     

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.     

Systems with outer constraints. Gupta-Bleuler electromagnetism as an algebraic field theory

Since there are some important systems which have constraints not contained in their field algebras, we develop here in aC*-context the algebraic structures of these. The constraints are defined as a groupG acting as outer automorphisms on the field algebra , :G Aut , _G Inn , and we find that the selection ofG-invariant states on is the same as the selection of states onM(G ) by (U _g)=1gG, whereU _g M (G )/ are the canonical elements implementing _g . These states are taken as the physical states, and this specifies the resulting algebraic structure of the physics inM(G ), and in particular the maximal constraint free physical algebra . A nontriviality condition is given for to exist, and we extend the notion of a crossed product to deal with a situation whereG is not locally compact. This is necessary to deal with the field theoretical aspect of the constraints. Next theC*-algebra of the CCR is employed to define the abstract algebraic structure of Gupta-Bleuler electromagnetism in the present framework. The indefinite inner product representation structure is obtained, and this puts Gupta-Bleuler electromagnetism on a rigorous footing. Finally, as a bonus, we find that the algebraic structures just set up, provide a blueprint for constructive quadratic algebraic field theory.     

Algebraic quantization of systems with a gauge degeneracy

Systems with a gauge degeneracy are characterized either by supplementary conditions, or by a set of generators of gauge transformations, or by a set of constraints deriving from Dirac's canonical constraint method. These constraints can be expressed either as conditions on the field algebra , or on the states on . In aC*-algebra framework, we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra . This factor algebra, , is free of state conditions. In this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions. The connection between states on and states on is investigated further within this framework, as is also the set of transformations which are compatible with the set of constraints. It is also shown that not every set of constraints can give rise to a nontrivial system. Finally as an example, the abstract theory is applied to the electromagnetic field, and this treatment can be generalized to all systems of bosons with linear constraints. The question of dynamics is not discussed.     

Construction and Borel summability of planar 4-dimensional euclidean field theory

We use the methods of [1] to show that the planar part of the renormalized perturbation theory for ₄ ⁴ -euclidean field theory is Borel-summable on the asymptotically free side of the theory. The Borel sum can therefore be taken as a rigorous definition of theN limit of a massiveN×N matrix model with a +trg ⁴ interaction, hence with wrong sign ofg. Our construction is relevant for a solution of the ultra-violet problem for planar QCD. We also propose a program for studying the structure of the renormalons singularities within the planar world.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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, . , . , , . , . .

     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

Symmetry transformations from local currents

For internal symmetries it is shown that it is possible to construct automorphisms for a Haag-Araki local ring system {(O)} from a local current affiliated to it. Although the chargesQ _v for finite volumeV do not converge forV we prove the convergence of the corresponding automorphisms of {(O)}. For external symmetries which map bounded space-time regions into unbounded ones (e.g. translations) we have to require some additional continuity condition on the isomorphisms corresponding toQ _v to get convergence.     

Upper limits for lepton-flavor violation from the exotic μ− ν e− conversion

The transition matrix elements for coherent and incoherent channels of the neutrinoless ^– e^– conversion are investigated. The results refer to the ²⁷Al nucleus which has recently been chosen as a target in the MECO experiment at Brookhaven aiming to search for -e conversion events with a sensitivity 10^-17. These results are compared to those obtained previously for ⁴⁸Ti and ²⁰⁸Pb targets. We focus on the contributions to the branching ratio e^– originating from scalar, vector and axial vector interactions resulting in conventional extentions of the standard model and minimal supersymmetric models with and without -parity violation. With our calculations we extract very severe constraints for the flavor violation parameters.     

Определение средней величины кристаллик ов кварца И графита на основани и первичной экстинкц ии

— —10 ^–4 —10 ^–2 . , . , , , , , .     

Новый тип рентгеновс кого спектрографа

. 1', . . .     

The quantum efficiency of the internal photo-electric effect in indium antimonide

A method is described for measuring the relative quantum efficiency of the internal photo-electric effect in semi-conductors by simultaneously measuring the photo-magnetoelectric and photo-conductive effect. The results of measurements on indium antimonide are given. The quantum efficiency begins to increase if the energy of the photon exceeds 0·47 eVat room temperature. The quantum efficiency as a function of the energy of the photon is analysed on the basis of the conception of impact ionization and it is shown that a study of the structure of this curve can supply information on the, band structure of a semi-conductor in the region of high energies of electrons and holes.

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. . , 0,47 eV . , .

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The authors thank M. Závtová and M. Vantuchová for efficient help with the measurements, K. mirous and V. Vrchovská for preparing the material, E. Antoník for critical remarks and M. Matyá and A. Müller for determining the constants of the material.     

BЛИЯHИE CBETA HA MOHOКPИCTAЛЛИЧECКИE ПЛACTИHКИ AgCl

The paper deals with the influence of light,=403 m, on the absorption of single-crystal plates of AgCl, grown by the capillary method. It was found that crystals with blue luminescence show no maximum in the region measured. For crystals with green luminescence a broad absorption maximum was found at – 590 m, which is partly bleached during further irradiation by light from the region of the absorption maximum. Measurements were preformed at room temperature.

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. .     

Trace states and KMS states for approximately inner dynamical one-parameter groups of *-automorphisms

The usual definition of approximately inner one-parameter groups of *-automorphisms ofC*-algebras (approximately inner dynamical one-parameter groups) contains a slight asymmetry. When this asymmetry is corrected, we show that if an approximately inner dynamical one-parameter group hasKMS states forone value of inverse temperature =1/kT, then it hasKMS states for all values of . By the Powers-Sakai Theorem it is enough to show that there is a trace state. We obtain a trace state as a limit of a sequence of vector states with respect to a givenKMS state and thus solve a problem raised in [6].Supported by Odense University, Denmark