Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

АНОМАЛЬНОЕ ПОГЛОЩЕН ИЕ ЗВУКА ПРИ ФАЗОВОМ ПЕРЕХОДЕ ВТОРОГО РОДА

The thermodynamic theory of transition in quartz is indicated and the results of studying the anomalous absorption of sound, which can be observed at the temperature of this transition, are summed up.     

MPT versus: A manifestly covariant presentation of motion reversal and particle-antiparticle exchange

We show that particle-antiparticle exchange and covariant motion reversal are two physically different aspects of the same mathematical transformation, either in the prequantal relativistic equation of motion of a charged point particle, in the general scheme of second quantization, or in the spinning wave equations of Dirac and of Petiau-Duffin-Kemmer. While, classically, charge reversal and rest mass reversal are equivalent operations, in the wave mechanical case mass reversal must be supplemented by exchange of the two adjoint equations, implying .Denoting by M the rest mass reversal, P the parity reversal, T the Racah time reversal, and Z the exchange, the connection with the usual scheme of charge conjugation, parity reversal, and Wigner motion reversal, is with, of course,     

A Strategy for a Vanishing Cosmological Constant in the Presence of Scale Invariance Breaking

Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace action becomes the statement 0 = Re Tr T , with T the operator stress energy tensor, and with Tr the trace over the underlying Hilbert space. We show that this condition implies the vanishing of the cosmological constant and vacuum energy in the emergent quantum field theory. However, since the scale invariance condition does not require the operator T to vanish, the spontaneous breakdown of scale invariance is still permitted.     

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.     

Non-Heisenberg states of the harmonic oscillator

The effects of the vacuum electromagnetic fluctuations and the radiation reaction fields on the time development of a simple microscopic system are identified using a new mathematical method. This is done by studying a charged mechanical oscillator (frequency ₀)within the realm of stochastic electrodynamics, where the vacuum plays the role of an energy reservoir. According to our approach, which may be regarded as a simple mathematical exercise, we show how the oscillator Liouville equation is transformed into a Schrödinger-like stochastic equation with a free parameter h with dimensions of action. The role of the physical Planck's constant h is introduced only through the zero-point vacuum electromagnetic fields. The perturbative and the exact solutions of the stochastic Schrödinger-like equation are presented for h>0. The exact solutions for which h<h are called sub-Heisenberg states. These nonperturbative solutions appear in the form of Gaussian, non-Heisenberg states for which the initial classical uncertainty relation takes the form (x ²)(p) ² =(h/2) ²,which includes the limit of zero indeterminacy (h 0). We show how the radiation reaction and the vacuum fields govern the evolution of these non-Heisenberg states in phase space, guaranteeing their decay to the stationary state with average energy h ₀ /2 and (x) ² (p) ² =h ² /4 at zero temperature. Environmental and thermal effects-are briefly discussed and the connection with similar works within the realm of quantum electrodynamics is also presented. We suggest some other applications of the classical non-Heisenberg states introduced in this paper and we also indicate experiments which might give concrete evidence of these states.     

Narrow-band electrons in transition-metal oxides

Experiments on LaCoO₃ demonstrate that crystal-field theory and band theory describe two thermodynamically different electronic phases. For an integral number of electrons per atom, the phase transition is first-order. The critical parameter is an overlap integral, which may be either a cation-cation or a cation-anion-cation overlap integral. Intra-atomic exchange and electron-phonon interactions contribute significantly to electron localization. The characteristic feature of collective electrons is a Fermi surface. Those physical properties that depend upon the existence of a Fermi surface vary discontinuously through a localized-electron collective-electron transition; other physical properties, including electron mobility and paramagnetic susceptibility, apparently do not. It is argued that the spontaneous crystallographic distortions associated with semiconducting metallic phase changes manifest the existence of narrow, cation-sublattice bands if the cations are removed from the centers of symmetry of their interstices, narrow crystalline bands otherwise; ferroelectric and antiferroelectric transitions manifest the existence of a narrow valence band; the formation of a homologous series of shear structures in nonstoichiometric compounds manifests narrow conduction bands. These distortions all result from the creation, or enhancement, of an energy discontinuity at the Fermi surface. By contrast, conventional Jahn-Teller distortions, magnetostriction due to spin-orbit coupling, and the ordering of small polarons manifest localized electrons and the applicability of crystal-field theory. It is also shown that the critical overlap integral (or bandwidth) for spontaneous band magnetism is only a little larger than that for a localized-electron collective-electron transition. Preliminary data are compatible with two possibilities for bands that are more than half-filled: (1) saturation of orbitals of spin, which leads to localized electrons of spin and collective electrons of spin; (2) spontaneous magnetization (ferromagnetism) of only the antibonding electrons, which may lead to reduced atomic moments. Spontaneous band antiferromagnetism may be stabilized in bands that are half-filled or slightly less. It is represented by a spin-density wave with wavelength adjusted to create an energy discontinuity at the Fermi surface. Spin-density waves are also possible among collective-spin electrons that are coupled to localized-spin electrons.Operated with support from the U.S. Air Force.     

The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

---

. . . , , .

---

---

The basic thesis of this paper, together with concrete calculation of the energy spectrum of diamond, was delivered at the Czechoslovak-Polish conference in Sopoty in November 1956.

---

In conclusion the autor would like to thank K. Trnková for carrying out the numerical calculations.     

Hyperfine interactions in muonium-impurity complexes in silicon

The properties of paramagnetic complexes formed by muonium located near acceptor and donor impurities in silicon are calculated using the quantum chemical methods. The calculated data are compared to the experimentally observed characteristics of normal and anomalous muonium centers.     

Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide

The propagation of electromagnetic surface waves along a radially inhomogeneous dielectric waveguide is investigated. The problem is formulated in terms of differential equations to be satisfied by the radially dependent parts of the electromagnetic field vectors. The dielectric waveguide is assumed to consist of a homogeneous cladding of infinite extent and a radially inhomogeneous core of higher permittivity. Numerical solutions of the differential equations in the core are obtained by two different methods, viz. by direct numerical integration and by substitution of an appropriate power series expansion. In the cladding the field is expressed in terms of modified Bessel functions. Imposing the boundary conditions at the interface of core and cladding, an equation for the unknown propagation coefficient is obtained. From this equation the propagation coefficients for the lower order modes are computed numerically. Numerical results are presented for some permittivity profiles of practical interest in single-mode transmission along optical fibres.Nomenclature a radius of the core - a _q vector coefficient in the power series expansion off() - A _i constants - A square matrix - b _q coefficient in the power series expansion of _r() - B square matrix - C square matrix - c _n unknown constant - d _n unknown constant - D() fundamental matrix - E,E _r,,z electric field vector and components - E,e _r,,z radially dependent parts ofe _r,,z - f solution vector - G _q square matrix - H,H _r,,z magnetic field vector and components - h _r,,z radially dependent parts ofE _r,,z - h reduced wavenumber - i radial mode number - j imaginary unit - k _0,m wave number - K _n modified Bessel function of the second kind and order n - n azimuthal mode number - t time - U normalized propagation constant - Z _m plane wave impedance of the cladding - r, , z cylindrical co-ordinates - p, q, s integers - propagation coefficient - increment - _0,m,r permittivity - normalized radiusr - ₀ wavelength in free space - ₀ permeability - angular frequency - d _r, differentiation with respect tor, Engineering and Professor H. J. Frankena of the Physics Department for their valuable discussions.     

All torsion-free spherical vacuum solutions of the quadratic Poincaré gauge theory of gravity

We find all torsion-free, spherically symmetric, vacuum solutions to the theory of gravity recently proposed by Hehl, Ne'eman, Nitsch, and von der Heyde. There are three classes of solutions: (A) the Schwarzschild metrics with arbitrary mass,M, and arbitrary cosmological constant, ; (B) the Nariai-Bertotti metrics with arbitrary positive cosmological constant, ; and (C) the conformally flat metrics whose conformai factor is ²/ ² where is a function of only the time coordinate , and the radial coordinate, and satisfies the wave equation in these variables. Hence there is no Birkhoff theorem for this theory. In fact, solutions (C) include some asymptotically flat but nonstationary solutions. On the other hand, solutions (A) include a gravitational confinement potential, as was sought by Hehl et al., since when <0, the weak field limit of the Schwarzschild metric becomes a harmonic oscillator potential. We also discuss the relationship of this theory to the Eddington theory, the Lichnerowicz-Kilmister-Newman-Yang theory, the Nordström theory and the Einstein theory with a cosmological constant.     

The thickness dependence of the domain structure of magnetoplumbite

The changes in domain structure as a function of the thickness of the crystal are studied on artificial magnetoplumbite crystals. The thickness dependence of the width of the domains is also studied; up to thicknesses of about 10 it follows the theoretical halfpower law. Above 10 the exponent is 0·633. The energy density of the Bloch walls=4·82 erg cm^–2 and the exchange constantA=0·66×10^–6 erg cm^–1 are calculated on the basis of the above measurements.

---

. , 10 . 0,633. = =4,82 erg m^–2 =0,66.10^–6 erg cm^–2.

---

---

We thank Z. Málek and V. Janovec for discussions and some remarks.     

Functional equation for dynamical zeta functions of Milnor-Thurston type

A Milnor-Thurston type dynamical zeta function _L (Z) is associated with a family of maps of the interval (–1, 1). Changing the direction of time produces a new zeta function _L (Z). These zeta functions satisfy a functional equation _L (Z) _L (Z)= ₀(Z) (where amounts to sign changes and, generically,₀1). The functional equation has non-trivial implications for the analytic properties of _L (Z).     

A study of the solid state-gaseous phase equilibrium in CdSe and its application to the growing of single crystals from the gaseous phase by Frerich's method

The equilibrium between the solid state and the gaseous phase of the semi-conducting compound CdSe is investigated. This is a study of two equilibrium reactions CdSe(s)Cd(g) + + (1/2) Se₂(g) and Se₆(g)3 Se₂(g) as a function of the temperature. The results were used to estimate the optimum conditions for the growing of CdSe single crystals from the gaseous phase by Frerichs' method. The basic electrical and optical properties were then measured on the crystals. In conclusion the results of the experiments are evaluated and compared with those of other authors.In conclusion, the authors thank Dr. E. Klier and other members of the department for much valuable advice and remarks, and laboratory assistants O. Kundrátová and J. Rejna for help in the work.     

Analytic structure of gauge fields

The analytic structure of gauge fields in the presence of fermions is studied in arbitrary symmetry. A Hamiltonian formalism is developed which relates Cauchy-Riemann equations to the symmetry. The formalism is applied to three problems in (2+1)-dimensional Euclidean space: (1) a free fermion, (2) a fermion interacting with a massless scalar field, and (3) a fermion interacting with a vector field. We find that the Hamiltonian for the free fermion is analytic and single-valued in a finite region of momentum space. With the addition of an auxiliary field, the Hamiltonian can be analytic in the entire momentum space. The scalar field then acquires spin-dependent coordinates by interaction with the fermion; the interactions break the Abelian symmetry of so that ₁ 1/(x₁ –-im ₁ ^–1 (x₁ –-im ₁ ^–1 ), wherem ₁ are spin-dependent and multivalued. There are four solutions for each chirality eigenvalue of the fermion. For spinless fermions gives the Jackiw-Nohl-Rebbi solution and is separable into Coulomb-like 1/x analytic functions on the first and fourth quadrants. For a vector field the results are similar except that the coordinates are not spindependent or multivalued; interactions break the initial symmetry andA (x )A ¹ (x ) and theA ¹ have a non-Abelian algebra. Thel indices represent directions fixed by spin matrices in a spin-dependent color space.     

Pregalactic black holes: A new constraint

Pregalactic black holes accrete matter in the early universe and produce copious amounts of x radiation. By using observations of the background radiation in the x and wavebands we have been able to impose a strong new constraint upon their possible abundance. If pregalactic black holes are actually present, several outstanding problems of cosmogony can be resolved with typical pregalactic black hole masses of 100M. Significantly more massive holes cannot constitute an appreciable mass fraction of the universe and are limited by _PGBH(M)<10(M JM)^–1.This essay received an honorable mention (1978) from the Gravity Research Foundation.     

Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

Boson-fermion duality in four dimensions: Comments on the paper of luther and schotte

The Fock space for the fermion field can be identified with the Fock space for the boson field, provided the overall numbers of internal degrees of freedom are the same. As a consequence, the respective free field Hamiltonian systems are equivalent (dual): the four-component neutrino model is thus equivalent to the doublet of independent (electric and magnetic, respectively) Maxwell fields, which are quantized in the Coulomb gauge. This statement arises on the field theory level, and seems to make doubtful the claim that realistic photons can be constructed from (bound) neutrino pairs: each (anti)neutrino degree should be represented by the photon-type (electric and magnetic, respectively) degree of freedom.     

The planckions as largest elementary particles and as smallest test bodies

Planck's units define the limits of super GUT and also the possibilities of classical measurements. A planckion' is the largest ultrarelativistic elementary particle and also the smallest body that can serve as a classical standard.     

К ТЕОРИИ ГРАВИТАЦИОННОГО ИЗЛУЧЕНИЯ

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

---

On the theory of gravitational radiation

The equations of motion of weakly radiating particles are investigated in a linear approximation in which the pseudo-Euclidian metric remains valid but energy changes caused by gravitational radiation are considered. The classical relativistic equations of motion with variable rest mass are applied. An elementary theory of the gravitational radiation of a rotator is formulated. The results are applied for particles in circular accelerators. It is found that a rotator with non-zero rest mass cannot exist for an unlimited period and that it cannot exceed the velocity of light. This explains why particles with non-zero rest mass cannot attain the velocity of light in circular accelerators; it is also shown that the gravitational radiation of particles in circular accelerators does not exist in practice.