Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

ИЗЛУЧЕНИЕ ЧЕРЕНКОВА ПРОСТРАНСТВЕННОГО З АРЯДА В ВОЛНОВОДАХ И В НЕОГР АНИЧЕННОЙ СРЕДЕ

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A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

On the photo-electroluminescence of ZnS-Cu

The influence of weak ultra-violet irradiation on the brightness waves of electroluminescence is investigated for two types of ZnS-Cuphosphors. The observed effects (increase in brightness in the primary peak and its phase shift, the disappearance of the secondary peak) are explained on the basis of present-day conceptions on electroluminescence.

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ZnS-Cu

ZnS-Cu. ( , ) .

     

On a class of equilibrium states under the Kubo-Martin-Schwinger boundary condition

Using the Kubo-Martin-Schwinger boundary condition for equilibrium states of quantum statistical mechanics of fermion gas, we prove that forT;0 a one-particle evolution (corresponding essentially to bilinear hamiltonians) generally defines a unique equilibrium state, which is quasi-free. Conversely any quasi-free state is the equilibrium state for a single one-particle evolution if it has no Fock part in its product decomposition. Limiting cases whereT 0 andT are studied. In the case whereT 0 one shows that the state generally converges to a Fock state linked to the evolution.Attaché de Recherche au C.N.R.S.This work is a part of a Thèse de Doctorat d'Etat presented to the Faculté des Sciences de Marseille, April 23, 1969, under the number A.O. 3073.     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

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The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

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 - — . , - , /. , , . , , , .

     

КРУЧЕНИЕ ПРИЗМАТИЧЕ СКИХ СТЕРЖНЕЙ ШВЕЛЛЕ РНОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

- [3], [4], U(x, y) . - U(x, y) -, . B § 10 - . , - , - D, . - .     

ЭЛЕКТРИЧЕСКИЕ И ТЕРМ ОЭЛЕКТРИЧЕСКИЕ СВОЙ СТВА АНТИМОНИДА ИНДИЯ

Qj , i 4 ISb, - N , –180° +400°C. , ISb zi, - ; -m _n =3,6. 10^–, n . menem , , - .eue . - - .     

Photo-luminescence and growth defects in ZnS: Cu monocrystals

The paper describes microscopic investigation into the spectral distribution of photo-luminescence and its polarization on hexagonal ZnS monocrystals in relation to the structural defects of such crystals. These observations, as well as birefringent observations, show that the values of the birefringence and the degree of polarization in different stripes of the same crystal are the same within the limits of observational errors.

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ZnS: Cu

ZnS . , , , .

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In conclusion the author would like to thank K. Pátek, L. Souková and M. Mokonová for providing the monocrystals and for fruitful discussions.     

Die Abhängigkeit der Banddurchbiegung von der Lage der Stufenversetzung

Zusammenfassung Es wird die Lösung des Spanungszustandes im unendlichen Band mit einer lotrecht zur Bandebene stehenden Stufenversetzung und mit einem Burgerschen Vektor, der parallel mit der Bandachse verläuft, unter der Voraussetzung der klassischen mathematischen Elastizitätstheorie wiedergegeben. Weiter wird der Ausdruck für die Gesamtdurchbiegung des Bandes in Abhängigkeit von der Lage der Versetzung und für die Durchbiegung bei einer allgemeinen Verteilung der Versetzungen, die durch eine kontinuierliche Verteilung approximiert ist, abgeleitet.

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Für die wertvolle Diskussion und einige Hinweise danke ich dem Kollegen Jan Kaczér, für das Lektorieren der Arbeit dem Kollegen Bohdan esták.     

Structural stability properties of friedman cosmology

A dynamical system with Robertson-Walker symmetries and the equation of the statep=, 01, considered both as a conservative and nonconservative system, is studied with respect to its structural stability properties. Different cases are shown and analyzed on the phase space (x=R ^D , y=x).     

B\bar B mixing with the bulk fields in the Randall-Sundrum model

We calculate mixing in the Randall-Sundrum bulk model. In this model, all the standard model fields except the Higgs field can reside in the bulk. Two suggestive models of mixed and relaxed scenarios are considered. We find that the enhancement of the loop function is 0.51% for the relaxed and 1.07% for the mixed scenario when the first four Kaluza-Klein modes are included, for a bulk fermion mass parameter .Received: 15 October 2003, Published online: 18 February 2004     

МОДЕЛИРОВАНИЕ ЭЛЕКТ РОННО-ОПТИЧЕСКИХ СИС ТЕМ С ОСЕВОЙ СИММЕТРИЕЙ П РИ ПОМОЩИ СЕТИ СОПРОТИВЛЕНИЙ

The paper explains the theory of modelling electrostatic fields by a resistance network. The conditions, which the resistance network must satisfy, are derived and the question of modelling electrodes of different shapes is solved. The finished network and the results obtained on it when modelling a jet for a linear h-f accelerator of electrons are described. Particular attention is paid to the influence of a space charge, the modelling of which is an advantage of this method.

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1- , 1964., , .

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On the law of approach to saturation in manganese-magnesium ferrite

The law of approach to saturation is studied for three differently porous samples of polycrystalline sintered Mn-Mg ferrite. Such an internal fieldH is sought that the dependenceI=I _s(1–a/H ²) might be satisfied. The changes which occu rin such a dependence, if the fieldH is changed by a certain multiple of the magnetization, ere investigated by calculation. Relations are derived for this case, which are satisfied very well by the experimental values. The properties of the effective anisotropy constants ara dealt with and, on the basis of temperature measurements, these constants are ascribed with very great probability to the internal form anisotropy.

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- Mn-Mg- . , I= I_S(1-a/H²). , , . , . .

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Reported on in the form of preliminary results in the Institute of Semi-conductors, Academy of Sciences, USSR, in Leningrad on 17. 10. 1960.

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In conclusion the author would like to thank Dr. S. Krupika, C. Sc., K. Závta, C. Sc., grad. phys. R. Gerber and grad. phys. E. Kratochvílová for valuable discussions and A. Hadincová for help in the measurements and for carefully making the numerical calculations and graphs.     

ПЛОТНОСТЬ ТОКА В АНОД НЫХ ПЯТНАХ ИСКРОВЫХ РАЗРЯДОВ В ВОЗДУХЕ ПР И АТМОСФЕРНОМ ДАВЛЕН ИИ

annapamyp, . .     

Измерение некоторых нейтронных спектров методом ядерных эмулъсий

. Ra+Be . , , . 8.     

ФИЗИЧЕСКИЕ ОСНОВЫ ИЗ МЕРЕНИЯ НАПРАВЛЕНИЯ ВОЗДУШНОГО ПОТОКА МЕ ТОДОМ НАКАЛЕННОЙ ПРО ВОЛОКИ ПРИ ВЫСОКНХ ПОДЗВУКО ВЫХ СКОРОСТЯХ

d - l - t _d R _max - J , ( ) - - , . . - ( ) - - R R _max —R. ,      

Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.