Evidence for nonperturbative string symmetries

String theory appears to admit a group of discrete field transformations — calledS dualities — as exact nonperturbative quantum symmetries. Mathematically, they are rather analogous to the better-knownT duality symmetries, which hold perturbatively. In this Letter the evidence forS duality is reviewed and some speculations are presented.     

Gravitational radiation of isolated systems

The gravitational radiation of isolated systems is studied by introducing a class of reference systems that is the analog of the class of inertial systems in flat space. Expressions for the total energy of these systems and the flux of gravitational radiation are obtained. The fundamental role of the Bondi-Metzner-Sachs asymptotic symmetry groups in the general theory of relativity is explained; transformations of the group characterize transitions from one reference system of a given class to another.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 47–54, November, 1973.     

Unit radius and the resolution of inverse square law forces

An equation for the solution of inverse square law forces that arise in rectilinear systems from gravitational, electrical, and magnetic fields, produced by complex multibody or multielement sources, is derived from a concept known asunit radius, which is associated with orbital systems, and the use of this equation in computer evaluation of simple models such as disks and spheres shows results that are in good agreement with those predicted by classical methods using a somewhat indirect approach. Additionally, these results show that, within the profile of the model so analyzed, the effective distance between the reference point and the resultant source is equal in all cases to the radius of the model, and that—again within the profile of the model—the magnitude of the resultant source varies directly with the distance of the reference point from the center of the model. Theproximity effect of sources of appreciable dimensions is examined in some detail and there is good evidence to show that as a result of this effect the resultant force when measured at the perimeter of a two-dimensional disk-shaped source is some 23% lower than the value anticipated by classical theory.     

Regularities of Bonding of Chlorin e 6 to the Oligomeric Enzyme Lactate Dehydrogenase

Using differential-spectrophotometry, spectral-luminescence, and polarization methods, we have investigated regularities of complexing of a promising photodynamic sensitizer — chlorin e ₆ — with a key glycolytic enzyme — lactate dehydrogenase (LDH). The parameters of the dye–enzyme complex have been estimated by the difference between the spectral characteristics of the free dye and the dye bonded to the enzyme. It is shown that the tetrameric LDH molecule forms an equilibrium complex with four chlorin molecules and the sensitizer is bonded independently to each subunit entering into the composition of the tetramer. It has been established that the spectral characteristics of chlorin bonded to LDH are sensitive to the structure transformations arising in the active center of the enzyme as a result of the formation of an unproductive enzyme–coenzyme–substrate complex, which allows the conclusion that the dye is localized in the neighborhood of the active center of LDH.     

Quantization as Selection Problem

Quantum systems exhibit a smaller number of energetic states than classical systems (A. Einstein, 1907, Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme, Ann. Phys. 22, 180ff). We take up the selection criterion for this in two parts. (1) The selection problem between classical and nonclassical mechanical systems is formulated in terms of possible and impossible configurations (among others, this overcomes the difficulties occurring when discussing the behavior of quantum particles in terms of paths). (2) The (nonclassical) selection of the quantum states is formulated, using recurrence relations and the energy law. The reformulation of “quantization as eigenvalue problem” in terms of “quantization as selection problem” allows one to derive Schrödinger’s stationary equation from classical mechanics through a straightforward and unique procedure; the nonstationary and multibody equations are subsequently acquired within the same frame. In contrast to the (classical) eigenvalue problem, the (nonclassical) selection problem can be formulated and solved without any reference to additional a priori assumptions on the nature of the quantum system, such as the wave-corpuscle dualism or an underlying wave equation or the existence of Planck’s finite action parameter. The existence of such an additional parameter—as the only additional one—is inherent in the procedure. Within our axiomatic-deductive approach, we modify classical mechanics only where it itself indicates an inherent limitation.     

On intrinsic randomness of dynamical systems

We discuss the problem of nonunitary equivalence, via positivity-preserving similarity transformations, between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes. Dynamical systems admitting such nonunitary equivalence with stochastic Markov processes are said to beintrinsically random. In a previous work, it was found that the so-called Bernoulli systems (discrete time) are intrinsically random in this sense. This result is extended here by showing that a more general class of dynamical systems—the so-calledK systems andK flows—are intrinsically random. The connection of intrinsic randomness with local instability of motion is briefly discussed. We also show that Markov processes associated through nonunitary equivalence tononisomorphic K flows are necessarily non-isomorphic.Dr. Goldstein's research was supported in part by NSF Grant No. PHY78-03816.     

The Inertial Transformations and the Relativity Principle

Our recently proposed inertial transformations of the space and time variables based on absolute simultaneity imply the existence of a single isotropic inertial reference system (“privileged system”). We show, however, that aresynchronization of clocks in all inertial systems is possible leading to a different, arbitrarily chosen,isotropic “privileged” system. Such a resynchronization does not modify any one of the empirical consequences of the theory,which is thus compatible with a formulation of the relativity principle weaker than adopted in Einstein’s theory of special relativity.     

Photopolymers — Holographic investigations,mechanism of recording and applications

The holographic characteristics of a broad class of photopolymerization systems of the acryl type — metal (Ba, Pb, Ca, Sr) acrylates and acrylamide — are investigated. The conditions — composition, recording light intensity and spatial frequency — for self-fixing real-time recording are defined. Holographic techniques are employed to determine some basic characteristics of the photopolymerization reactions — order of the photochemical reaction and diffusion coefficients of the monomers used. Experiments are carried out proving the suitability of the investigated photopolymerization systems for optical correlation processing.     

Lax Pair Tensors and Integrable Spacetimes

The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a well-known Lax representation—the three-particle open Toda lattice—is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certain Riemannian geometry. By using different canonical transformations we obtain two inequivalent geometries which both represent the original system. Adding a timelike dimension gives four-dimensional spacetimes which admit two Killing vector fields and are completely integrable.     

Quantum behavior of deterministic systems with information loss: Path integral approach

’t Hooft’s derivation of quantum from classical physics is analyzed by means of the classical path integral of Gozzi et al. It is shown how the key element of this procedure—the loss of information constraint—can be implemented by means of Faddeev–Jackiw’s treatment of constrained systems. It is argued that the emergent quantum systems are identical with systems obtained in Blasone et al. [Phys. Rev. A 71 (2005) 052507] through Dirac–Bergmann’s analysis. We illustrate our approach with two simple examples—free particle and linear harmonic oscillator. Potential Liouville anomalies are shown to be absent.     

Effect of a massive reference system on the readings of measuring instruments

In an earlier paper a new group of coordinate transformations was obtained for reference systems tied to massive bodies. In the present paper a relation is established between the metric coefficients of such systems and the energy of the signal. The effect of the reference body on the readings of the measuring instruments is considered with the example of the Doppler effect.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 67–71, July, 1979.In conclusion, I would like to express my indebtedness to Professor D. D. Ivanenko for his interest in the paper and his valuable comments.     

Antiparticles from special Relativity with ortho-chronous and antichronous Lorentz transformations

Special Relativity can be based on the whole proper group of both ortho- and antichronous Lorentz transformations, and a clear physical meaning can be given also to antichronous (i.e., nonorthochronous) Lorentz transformations. From the active point of view, the latter requires existence, for any particle, of its antiparticle within a purely relativistic, classical context. From the passive point of view, they give rise to frames dual to the ordinary ones, whose properties—here briefly discussed—are linked with the fact that in relativity it is impossible to teach another, far observer (by transmitting only instructions, and no physical objects) our own conventions about the choices right/left, matter/antimatter, and positive/negative time direction. Interesting considerations follow, in particular, by considering—as it is the case—theCPT operation as an actual (even if antichronous) Lorentz transformation.Work partially supported by FAPESP and CNPq (Brazil).     

The notions of symmetry and computational feedback in the paradigm of steady,simultaneous quantum computation

Digital computation—i.e., the coherent concatenation of logicalif/then statements—is generally mapped onto the temporal transformation of a physical state. In the alternative paradigm of steady, simultaneous quantum computation, logical concatenations are mapped onto the transformations of a quantum steady state into itself. Such transformations, separated from the time variable and thus freed from the one-way progression of time, can mapcircular logical concatenations. This gives rise to nondeterministic and nonrecursive computation. Toy model Hamiltonians of elementary (steady) computations are given to exemplify the applicability of the paradigm.     

Photoinduced Oxidation of Diphenylbisanthene and Its Spectral Manifestations

The absorption and fluorescence spectra of diphenylbisanthene (DPB) in n-octane and benzene at 300 and 77 K have been investigated. The appreciable Stokes shift of the fluorescence band (180 cm^–1 in n-octane and 440 cm^–1 in benzene) points to the nonplanar character of the aromatic skeleton of DPB, which has been confirmed by results of the optimization of the molecule geometry by the AMI quantum-mechanical method. It has been found that spectral manifestations of the products of photoinduced transformations of DPB molecules are observed in the UV region (200–350 nm), and it has been shown that the observed photochemical process is two orders of magnitude less effective than for diphenylhelianthrene. On the basis of the experimental data and the results of the quantum-chemical calculations of the electronic spectra of molecules of DPB and endoperoxides (ZINDO/S method), it has been concluded that the end products of DPB phototransformations are its endobiperoxides in which —O—O— groups are added to the phenyl-substituted benzene rings of the aromatic skeleton.     

Algebraically Self-Consistent Quasiclassical Approximation on Phase Space

The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary * operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation of Thomas–Fermi theory, and a new quantization rule which—unlike semiclassical quantization—is non-invariant under action transformations of the Hamiltonian, in the same qualitative manner as the true eigenvalues. The quasiclassical eigenvalues are shown to be significantly more accurate than the corresponding semiclassical values, for a variety of 1D and 2D systems. In addition, certain standard refinements of semiclassical theory are shown to be easily incorporated into the quasiclassical formalism.     

Entropy and Ergodicity of Boole-Type Transformations

We review some analytic, measure-theoretic and topological techniques for studying ergodicity and entropy of discrete dynamical systems, with a focus on Boole-type transformations and their generalizations. In particular, we present a new proof of the ergodicity of the 1-dimensional Boole map and prove that a certain 2-dimensional generalization is also ergodic. Moreover, we compute and demonstrate the equivalence of metric and topological entropies of the 1-dimensional Boole map employing “compactified”representations and well-known formulas. Several examples are included to illustrate the results. We also introduce new multidimensional Boole-type transformations invariant with respect to higher dimensional Lebesgue measures and investigate their ergodicity and metric and topological entropies.     

Commensurability magneto-resistance peaks in a lattice of diffusive scatterers

Commensurability peaks in new kind of two-dimensional (2D) systems with artificial scatterers—2D electron gas in the array of diffusive and thermalizing scatterers (it was AuGeNi alloy dots)—was studied experimentally. It is shown that the position and the amplitude of these peaks are completely described by the model of pin-ball electron trajectories.     

The introduction of Superluminal Lorentz transformations: A revisitation

We revisit the introduction of the Superluminal Lorentz transformations which carry from bradyonic inertial frames to tachyonic inertial frames, i.e., which transform time-like objects into space-like objects, andvice versa. It has long been known that special relativity can be extended to Superluminal observers only by increasing the number of dimensions of the space-time or—which is in a sense equivalent—by releasing the reality condition (i.e., introducing also imaginary quantities). In the past we always adopted the latter procedure. Here we show the connection between that procedure and the former one. In other words, in order to clarify the physical meaning of the imaginary units entering the classical theory of tachyons, we have temporarily to call into play anauxiliary six-dimensional space-time M(3, 3); however, we are eventually able to go back to the four-dimensional Minkowski space-time. We revisit the introduction of the Superluminal Lorentz transformations also under another aspect. In fact, the generalized Lorentz transformations had been previously written down in a form suited only for the simple case of collinear boosts (e.g., they formed a group just for collinear boosts). We express now the Superluminal Lorentz transformations in a more general form, so that they constitute a group together with the ordinary—orthochronousand antichronous—Lorentz transformations, and reduce to the previous form in the case of collinear boosts. Our approach introduces either real or imaginary quantities, with exclusion of (generic) complex quantities. In the present context, a procedure—in two steps—for interpreting the imaginary quantities is put forth and discussed. In the case of a chain of generalized Lorentz transformations, such a procedure (when necessary) is to be applied only at the end of the chain. Finally, we justify why we call transformations also the Superluminal ones.     

Experimental investigation of extinction cross-section of single vegetation elements using open resonator

The experimental results of investigation of the total cross — section of scattering and absorption (extinction cross — section) _t of stalks and strip leaves of grass in millimeter waves range are presented. The investigation was carried out using open quasioptical resonator with spherical mirrors. Measirements were carried out as by absolute method as using the relative method. Experimental results obtained by two different methods showed that in spite of some data differences obtained by absolute and relative methods the latter may be used for estimation of the extinction cross — section _t of vegetation elements.