A topological characterization of classical BRST cohomology

The recent identification of classical BRST cohomology with the vertical cohomology of a certain fibration is used to compute it in terms of the classical observables and the topology of the gauge orbits. When the gauge orbits are compact and orientable, a duality theorem is exhibited.     

Carrier lifetime in single-crystal PbS films

The temperature dependence of the majority carrier lifetime was studied in single-crystal PbS films. In n- and p-type films in the range 300-200 ° K, increases exponentially with decreasing temperature, with an activation energy of e O. 17-0. 2 eV. This m dependence is assumed due to the trapping of minority carriers at deep levels. Below 160 ° K in the n-type films, does not depend on the temperature, while in the p-type films, decreases exponentially with an activation energy of 0. 11–0. 14 eV.Translated from Vysshikh Uchebnykh Zavedenii Fizika, No. 6, pp. 64–67, June, 1970.     

БЕТАТРОННЫЕ КОЛЕБАН ИЯ В УСКОРИТЕЛЕ С ОБЩИМ ПОЛЕМ I

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Betatron oscillations in an accelerator with a general field I

The paper gives a linear theory of equilibrium trajectories in an accelerator with a generalized magnetostatic field, the components of which are defined on a general rotation surface. Equations of motion of the particles in natural coordinates are derived with respect to the change in energy and dissipative force. A system of equilibrium trajectories is found in the general form. Conditions for the field components on the reference surface, necessary for the existence of equilibrium trajectories, for the conservation of their geometric similarities and for maintaining the constancy of the frequencies of the betatron oscillations, are derived. A condition is also derived which must be satisfied by the reference surface in order to conserve constant circular frequency of the particles. It is seen that it is not possible to find a field for an accelerator with an exactly constant circular frequency and with constant frequencies of the betatron oscillation in the relativistic energy region. An ultra-relativistic cyclotron with such properties is realizable.

     

Asymptotic theory of multidimensional chaos

A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.     

On measurement and irreversible processes

The nature of physical measurements performed on microscopic systems is discussed, and it is suggested that the procedures which are conventionally referred to as measurements fall into at least three different categories. The connection between observation processes and irreversible processes is stressed. The customary quantum mechanical treatment of irreversible processes is discussed, and its deficiencies from the philosophical point of view are criticized. The standpoint that quantum mechanics should not be considered as a basic philosophical system but rather as an immensely useful tool is defended. Some attempts at developing a more basic theory are discussed, and a hypothesis is put forward concerning the role of entropy within some possible future nonlocal hidden-variable theory.     

Piron's axioms for quantum mechanics: A reply to Foulis and Randall

In their paper A note on Misunderstandings of Piron's Axioms for Quantum Mechanics, Foulis and Randall undertake a reply to our critique of Piron's question-proposition system (qp-s) which appeared in previous issues of this journal. In the present paper, we want briefly to refute the points of criticism raised by Foulis and Randall (FR). We argue that the misunderstandings are not ours, and we prove it.     

Remarks on mathematical structure of BRST theories

A number of rigorous results concerning the mathematical structure of quantum systems with the BRST symmetry are presented. For studying model-independent properties of such systems, a generalization of the Strocchi-Wightman theory is suggested, which is a Wightman type theory in the Krein space with an OpJ*-algebra of physical and ghost fields. It is proved that the BRST charge operatorQ is either bounded with (Q)={0} or unbounded with (Q)=¢. A number of conditions equivalent to the no-ghost theorem (which states that the kernel ofQ is non-negative) are derived.     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

Magnetization coils without iron core for high field intensities

A new theory of rectangular coils without an iron core is described which amends the old one of Fabry and Bitter. It enables us to compute field intensities in coils having very small openings, which the old theory could not do.

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ПРИМЕНЕНИЕ ПАРАМАГН ИТНОГО РЕЗОНАНСА ДЛЯ ИССЛЕДОВАНИЯ РЕАКЦИЙ СВОБОДНЫХ РА ДИКАЛОВ

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The use of paramagnetic resonance in studying the reactions of free radicals

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The influence of a small electric perturbation on the electroluminescence curve of ZnS-Cu

The influence of a small electric perturbation of variable phase on the brightness wave of alternating electroluminescence of ZnS-Cu is investigated. The results are compared with the model described in [1]. The increase in the number of ionized activators after switching on the electric field is studied and is found to reach equilibrium. after about 50 to 150 sec.

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ZnS-Cu

ZnS-Cu. , [1]. , 50–150 s.

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In conclusion the author thanks M. Mokonová for cooperation in evaluating the results of measurement.     

On the zigzagging causility model of EPR correlations and on the interpretation of quantum mechanics

Being formalized inside the S-matrix scheme, the zigzagging causility model of EPR correlations has full Lorentz and CPT invariance. EPR correlations, proper or reversed, and Wheeler's smoky dragon metaphor are respectively pictured in spacetime or in the momentum-energy space, as V-shaped, A-shaped, or C-shaped ABC zigzags, with a summation at B over virtual states |B B|. An exact correspondence exists between the Born-Jordan-Dirac wavelike algebra of transition amplitudes and the 1774 Laplace algebra of conditional probabilities, where the intermediate summations |B) (B| were over real hidden states. While the latter used conditional (or transition) probabilities (A|C) = (C|A), the former uses transition (or conditional) amplitudes A|C = C|A*. The formal parrallelism breaks down at the level of interpretation because (A|C) = |A|C|². CPT invariance implies the Fock and Watanabe principle that, in quantum mechanics, retarded (advanced) waves are used for prediction (retrodiction), an expression of which is | U | = | U = U|, with | denoting a preparation, | a measurement, and U the evolution operator. The transformation | = |U or | = |U^–1 exchanges the preparation representation and the measurement representation of a system and is ancillary in the formalization of the quantum chance game by the wavelike algebra of conditional amplitude. In 1935 EPR overlooked that a conditional amplitude A|C = A|BB|C between the two distant measurements is at stake, and that only measurements actually performed do make sense. The reversibility A|C = C|A* implies that causality is CPT-invariant, or arrowless, at the microlevel. Arrowed causality is a macroscopic emergence, corollary to wave retardation and probability increase. Factlike irreversibility states repression, not suppression, of blind statistical retrodiction—that is, of final cause.Dedicated to Professor David Bohm, proponent of the EPRB version of nonseparability.     

Paramagnetic resonance of Fe3+ ion in CdWO4 monocrystal

The paramagnetic spectrum of the Fe³⁺ ion in a CdWO₄ monocrystal was measured on a frequency of 9600 kMHz at 290°K. The spin-Hamiltonian of the Fe³⁺ ion was determined and had the form of (1). The constants derived for the spin-Hamiltonian areE/D=0·144±0·002,D=23·8 kMHz.

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Fe³⁺ CdWO₄

Fe³⁺ CdWO₄ 9600 kMHz 290°K. - Fe³⁺ (1), E/D 0,144±0,002 D 23,8 kMHz.

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In conclusion, the authors thank . Bárta and V. Kment from the Society for Chemical and Metallurgical Production in Ústí n/L for producing and supplying the monocrystals and for much valuable advice.     

Absence of self-averaging of the order parameter in the Sherrington-Kirkpatrick model

We prove that if _N is the Sherrington-Kirkpatrick (SK) Hamiltonian and the quantity converges in the variance to a nonrandom limit asN, then the mean free energy of the model converges to the expression obtained by SK. Since this expression is known not to be correct in the low-temperature region, our result implies the non-self-averaging of the order parameter of the SK model. This fact is an important ingredient of the Parisi theory, which is widely believed to be exact. We also prove that the variance of the free energy of the SK model converges to zero asN, i.e., the free energy has the self-averaging property.See the Remarks after the proof of Theorem 1 on the validity of our results for more general distributions ofJ _ij .     

Absolute Spacetime: The Twentieth Century Ether

All gauge theories need somethingfixed even as something changes.Underlying the implementation of these ideas all majorphysical theories make indispensable use of anelaborately designed spacetime model as the something fixed,i.e., absolute. This model must provide at least thefollowing sequence of structures: point set, topologicalspace, smooth manifold, geometric manifold, base forvarious bundles. The fine structure ofspacetime inherent in this sequence is of courseempirically unobservable directly, certainly whenquantum mechanics is taken into account. This issue isat the basis of the difficulties in quantizing generalrelativity and has been approached in many differentways. Here we review an approach taking into account thenon-Boolean properties of quantum logic when forming a spacetime model. Finally, we recall how thefundamental gauge of diffeomorphisms (the issue ofgeneral covariance vs. coordinate conditions) raiseddeep conceptual problems for Einstein in his earlydevelopment of general relativity. This is clearlyillustrated in the notorious holeargument. This scenario, which does not seem to bewidely known to practicing relativists, is neverthelessstill interesting in terms of its impact for fundamental gaugeissues.     

Non-gravitational force effect in general theory of relativity

Equations are derived from the variational principle for a system subjected to an additional non-gravitational force effect, which may be represented by the technical forces imparting to the masses of the system a velocity comparable with the velocity of light and which may change the rest mass of the system, within the framework of the general theory of relativity.

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Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

Approximate calculation of frequencies of localized vibrations

An exact calculation of the frequencies of localized vibrations in a crystal with defects meets with considerable difficulties and therefore only the simplest cases have been calculated [9, 10]. An approximate calculation is confined to computing the frequencies of a system composed of several atoms in the neighbourhood of the defect. The interaction between this system and the other atoms of the lattice, which however are immobile in this approximation, is taken into consideration. Since the analytical estimate of the approximation is very rough, the approximate and exact calculations have been compared for some concrete cases (Fig. 1, 2). It is clear from these calculations that the use of the proposed approximation leads to good results.

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Propagator,sewing rules,and vacuum amplitude for the Polyakov point particle with ghosts

We apply techniques developed for strings to the case of the spinless point particle. The Polyakov path integral with ghosts is used to obtain the propagator and one-loop vacuum amplitude. The propagator is shown to correspond to the Green's function for the BRST field theory in Siegel gauge. The reparametrization invariance of the Polyakov path integral is shown to lead automatically to the correct trace log result for the one-loop diagram, despite the fact that naive sewing of the ends of a propagator would give an incorrect answer. This type of failure of naive sewing is identical to that found in the string case. The present treatment provides, in the simplified context of the point particle, a pedagogical introduction to Polyakov path integral methods with and without ghosts.     

Generalized classical BRST cohomology and reduction of Poisson manifolds

In this paper, we formulate a generalization of the classical BRST construction which applies to the case of the reduction of a Poisson manifold by a submanifold. In the case of symplectic reduction, our procedure generalizes the usual classical BRST construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold, i.e. the case of reducible first class constraints. In particular, our procedure yields a method to deal with second-class constraints. We construct the BRST complex and compute its cohomology. BRST cohomology vanishes for negative dimension and is isomorphic as a Poisson algebra to the algebra of smooth functions on the reduced Poisson manifold in zero dimension. We then show that in the general case of reduction of Poisson manifolds, BRST cohomology cannot be identified with the cohomology of vertical differential forms.Address after September 1992