Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

Algebraic quantization,good operators and fractional quantum numbers

The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the failure of the Ehrenfest theorem is clarified in terms of the already defined notion ofgood (andbad) operators. The analysis of constrained Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for quantum operators without classical analogue and for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring anomalous operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively.Work partially supported by the DGICYT.     

One massless particle equals two Dirac singletons

The remarkable representations of the 3+2 de Sitter group, discovered by Dirac, later called singleton representations and here denoted Di and Rac, are shown to possess the following truly remarkable property: Each of the direct products Di Di, Di Rac, and Rac Rac decomposes into a direct sum of unitary, irreducible representations, each of which admits an extension to a unitary, irreducible representation of the conformal group SO(4, 2). Therefore, in de Sitter space, every state of a free, massless particle may be interpreted as a state of two free singletons — and vice versa. The term massless is associated with a set of particle-like representations of SO(3, 2) that, besides the noted conformal extension, exhibit other phenomena typical of masslessness, especially gauge invariance.     

From where do quantum groups come?

The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other () expressing the quantum groups as deformation of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the -deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.Dedicated to Asim Barut with all our friendship.     

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.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Quantitative method for determination of fibre texture in wires I. Principle of method and analytical expression of absorption factor

An X-ray diffraction method is described for the quantitative determination of the fibre texture in cylindrical specimens (wires), which does not require specimen preparation. The integrated intensity of the diffracted radiation from a certain atomic plane is measured in the direction parallel to the plane determined by the axis of the wire and by the direct beam for different orientations of the axis of the wire. These measurements can be carried out in practice using an X-ray counter diffractometer or Weissenberg goniometer. The pole figure is determined from the dependence of the diffracted intensity on the orientation of the wire after correcting the intensities for the absorption of radiation in the specimen. The geometric arrangement enables the absorption factor to be calculated analytically. Its form was verified experimentally by measuring the dependence of the intensity of the 220 reflection on the orientation of the axis of a cylindrical specimen of Al containing randomly oriented crystals.

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I.

( ), . , , , . . , . . 220 .

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The author wishes to thank Z. iký for help in carrying out the measurements and calculations.     

The unitary bogoliubov transformation for a quantized scalar field in a friedman space-time

The time-dependent creation and annihilation operators for a complex scalar field, in a Friedmann space-time, defining particle states with respect to which the Hamiltonian is diagonal, are related by a Bogoliubov transformation to the creation and annihilation operators defined in strict analogy with the procedure carried out in Minkowski space. The Bogoliubov transformation is here written in terms of a unitary operator,U, and an expression for that operator is found via the generating functionF=i InU. The properties of the representation obtained by makingU act upon the state vector , to give a new state _U, are discussed. It is shown that the particle-number operator remains constant in such a picture so that the evolution of the system with time is clearly seen to depend upon the energy _k on the one hand, and upon the state vector _U on the other. Also, it is pointed out that this new representation permits the in and out states to be defined unambiguously.On leave of absence from Istituto de Fisica G. Galilei (Padova) and Istituto Nazionale di Fisica Nucleare (Sezione di Padova).     

Effect of electrolytically deposited nickel films on the magnetic properties of iron-silicon alloy

The effect of electrolytically deposited nickel films on the magnetostriction, coercive force, residual induction, and the position with respect to each other of the magnetic susceptibility maxima _max. _max of specimens of iron-silicon alloy is investigated. It is shown that elastic extensions lead to a reduction in the spacing between the maxima _max, _max , and for certain loads this spacing disappears and only one maximum is observed.     

ИЗМЕРЕНИЕ НАПРЛЖЕНН ОСТИ МАГНИТНОГО ПОЛЯ МЕТОДОМ ПАРАМАГНИТН ОГО РЕЗОНАНСА

, 250–3000 .     

Domain structure of cobalt whiskers

An experimental investigation is made into the domain structure of cobalt whiskers by the colloid technique. A new type of domain structure was found; the width of the domains is studied as a function of the thickness of the whisker. This dependence follows a two-thirds power law and does not agree with existing theories which predict a half power law.

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. . , .

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In conclusion the authors wish to thank V. Janovec and F. Kroupa for valuable remarks and A. Tahalová for help in growing the whiskers.     

A note on the Watanabe theory of weak interactions

It is shown that according to the Watanabe theory of weak interactions a resonant scattering of electrons by protons must take place. The resonant energy depends on the massm _B of the intermediate boson. Form _B=2300m _e this energy is about 213 MeV in the centre of the mass system (c. m. s.). The energy width at resonance is 1·4 MeV.

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, . , , . _{m B}=2300_{m B} , 213 MeV -. 1,4 MeV.

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The author would like to thank Professor V. Votruba for suggesting this note and for valuable advice and help during the work.     

Contribution to the theory of single-mode laser modulation II. Conduction modulation

The problem of conduction modulation of laser radiation is considered. It is shown that acoustic wave interacting with photon field in active medium causes a periodic modulation of the number of quanta in the single-mode gas laser. The problem of modulation is solved quantum mechanically and it is shown that dielectric and conduction modulation give similar results.     

К ТЕОРИИ СПОНТАННОЙ Н АМАГНИЧЕННОСТИ ТОНКИХ СЛОЕВ. II. ЧАСТЬ)

- , . - . - - . , . 1956 .     

Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq ² (t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.     

АНТИПРОТОННАЯ СХЕМА β-РАСПАДА

, .     

Acoustomagnetoelectric current effects on mesoultrasound in anisotropic semiconductors

The acoustomagnetoelectric (AME) current effects on mesoultrasound in monopolar single-valley semiconductors with anisotropic scattering in arbitrary classical magnetic fields are computed analytically. The specimen is considered short-circuited along the q-wave vector of the ultrasound (US) wave. Two configurations are examined: 1) q is directed at an arbitrary angle 9 to the axis of highest order crystal symmetry C₆ (z axis), the y axis to the (q, C₆) plane, the magnetic field B lies in the (q, y) plane at an arbitrary angle to the vector q. Two transverse AME field components are calculated: along y and in the (q, C₆) plane. They express the Hall effects at mesoultrasound, the planar and normal, 2) q is directed along the y axis while B is in the (x, z) plane at an angle to the C₆(z) axis. The AME field component along B, the Grobner effect at mesoultrasound, is calculated. The dependence of the effects onB is studied and their estimate is given in weak and strong fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 57–61, July, 1989.     

On the “projective” magnetohydrodynamics

In the projective relativity based on the de Sitter universe, Maxwell's generalized theory gives us the magnetohydrodynamics, valid on a cosmic scale, for hyperdense matter and high energies. From the new theory can be deduced as limiting cases the hydrodynamics and thermohydrodynamics, the ideal magnetohydrodynamics, the electromagnetism, and the electrohydrodynamics, invariants for the projective Fantappié group.     

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.     

Spherically Symmetric Space-Time with Two Cosmological Constants

We present the analytic spherically symmetric solution of the Einstein equations, which has de Sitter asymptotics for both r and r 0. This two-lambda spherically symmetric solution is globally regular. At the range of mass parameter M_cr1 < M < M_cr2 it has three horizons and describes a neutral black hole whose singularity is replaced by a cosmological constant of Planck or GUT scale, at the background of small . Global structure of space-time contains an infinite sequence of black and white holes, de Sitter-like past and future regular cores (with + at r 0) replacing singularities, asymptotically de Sitter external universes (with for r ), and spacelike infinities. In the range of mass parameter M < M_cr1 we have a one-horizon solution describing recovered selfgravitating particle-like structure at the background of small , and for M > M_cr2 another one-horizon configuration which can be called de Sitter bag. The solutions with M = M_cr1 and M = M_cr2 represent two extreme states of a neutral nonsingular cosmological black hole.