The inverse scattering method in an invariant form with respect to internal symmetry algebra representations

By the example of the sine—Gordon equation, we develop a technique for obtaining soliton solutions. This procedure is not connected with a concrete matrix realization of the Lax pair operators but it directly appeals to the properties of internal symmetry spectrum of the corresponding equations.     

q-deformed Minkowski space based on a q-Lorentz algebra

The Hilbert space representations of a non-commutative -deformed Minkowski space, its momenta and its Lorentz boosts are constructed. The spectrum of the diagonalizable space elements shows a lattice-like structure with accumulation points on the light-cone. Received: 23 January 1997 / Published online: 10 March 1998     

New form of dynamics and current algebra

We study a new form of dynamical system, in which the commutation relations for the dynamical variables of a quantized field are defined on a “lightlike surface $\text{τ≡}\text{(t+z)}\text{2}\text{=0}$ rather than at one instant of time t = 0. We clarify the physical implications of the use of the new variables x¹ = x, x² = y, $\text{x}{}^{\mathrm{+}}\text{=}\text{(t+z)}\text{2}\text{, x}{}^{\mathrm{?}}\text{=}\text{(t?z)}\text{2}$ and explore its significance as a new form of relativistic dynamics, which holds in any Lorentz frame but not in the so-called “infinite momentum frame.” Using the quark model, we build up a new algebra of currents, in which the current commutators are defined at equal τ. The sum rules and other results of the usual current algebra can be obtained without taking the unjustifiable limit of infinite momentum. In particular, we obtain the Gell-Mann-Okubo mass formulas in quadratic form for both mesons and baryons without the trouble due to momentum dependence. We derive the reduction formula and find the physical high energy limit (not the Bjorken limit) of an amplitude is determined by the equal τ commutator.     

Polynomial form of the Hilbert–Einstein action

Configuration space of general relativity is extended by inclusion of the determinant of the metric as a new independent variable. As the consequence the Hilbert–Einstein action takes a polynomial form.     

Hilbert space representation of an algebra of observables forq-deformed relativistic quantum mechanics

Using a representation of theq-deformed Lorentz algebra as differential operators on quantum Minkowski space, we define an algebra of observables for a q-deformed relativistic quantum mechanics with spin zero. We construct a Hilbert space representation of this algebra in which the square of the massp ² is diagonal.     

Instability of horizon with respect to perturbation by a scalar field

The inverse effect on the metric in the case of collapse with a spherically symmetric nonstatic scalar field is investigated. It is shown that there is not sufficient reason to neglect this effect in this case.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 115–119, March, 1978.The author is grateful to V. P. Frolov for stimulating comments and to the participants of Professor D. D. Ivanenko's seminar for discussing this paper.     

Gain optimization with respect to the thickness of a sillenite crystal

Simple analytical expressions for the dependence of the maximum gain on the polarization angle of the interacting light waves and the crystal thickness are obtained for two-wave mixing in a cubic optically active piezoelectric crystal. By applying the theory to Bi₁₂SiO₂₀ and Bi₁₂TiO₂₀ crystals, the optimum gain is found also with respect to the grating orientation. The r?le of the (inverse) piezoelectric effect is investigated. Received: 23 November 1998 / Revised version: 8 January 1999 / Published online: 7 April 1999     

Current algebra of quarks confined to a cavity

Equal-time commutators of fields with charges are calculated in a cavity approximation to the MIT bag model, with N flavours of non-interacting quarks confined to a rigid spherical cavity and SU(N) symmetry arbitrarily broken by mass terms. It is proved that inside the cavity the algebra is identical with that of free field theory, whilst on the boundary quark fields commute with axial charges. Vector divergences and sigma commutators belong to a $\text{(N,}\text{N}\text{) + (}\text{N}\text{, N)}$ multiplet of chiral SU(N) × SU(N). Axial divergences contain additional surface terms which do not contribute to sigma commutators. A non-strange quark mass in the range 20–44 MeV is required to give a value 30–70 MeV for the nucleon matrix element of the sigma commutator relevant to pion-nucleon scattering.     

Equilibrium with respect to pair creation in a quantizing magnetic field

The influence of quantizing magnetic fields on the production of electron-positron pairs in a hot equilibrium magnetized plasma is estimated. It is shown that with increasing strength of the external frozen magnetic field the concentration of electron-positron pairs increases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 122–126, September, 1977.     

Statistical approach to calculation of lifetime with respect to annihilation of a positron-anion system

The lifetimes with respect to annihilation of bound positron-anion systems are calculated in the framework of a statistical model of an atom with consideration of anion electrons. To find the positron wave function, a variational procedure with allowance for the explicit form of the potential that acts on the positron in the anion is used. Calculated lifetimes are compared with Hartree-Fock calculations for some halogen ions. Ways of comparing the results of the theory with experiment are noted.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 49–53, February, 1991.     

Average coherence with respect to complementary measurements

We investigate the average coherence with respect to a complete set of complementary measurements.By using a Wigner-Yanase skew information-based coherence measure introduced in Luo and Sun(2017 Phys.Rev.A 96,022130),we evaluate the average coherence of a state with respect to any complete set of mutually unbiased measurements and general symmetric informationally complete measurements,respectively.We also establish analytically the relations among these average coherences.     

The BRS algebra of a free minimal differential algebra

We construct the Weil and the universal BRS algebras of theories that can have as a gauge symmetry a free minimal differential (Sullivan) algebra, the natural extension of Lie algebras allowing the definition of p-form gauge potentials (p > 1). The geometrical meaning of these p-form gauge potentials can be understood with the notion of a Quillen superconnection.     

Scaling with respect to disorder in time-to-failure

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of time-to-rupture and of the amplitude of the disorder, which allows us to collapse neatly the numerical simulations over more than five decades in time and more than one decade in disorder amplitude onto a single master curve. We thus conclude that, at least in this model, dynamical rupture in systems with long-range elasticity is a genuine critical phenomenon occurring as soon as the disorder is non-vanishing. Received: 11 July 1997 / Revised: 6 November 1997 / Accepted: 10 November 1997     

Reactivity of hydrogen peroxide with respect to ozone

Ozone decomposition in pure water, H₂O₂ aqueous solution, and water with ethanol admixture is investigated. It is found that, in the presence of H₂O₂, ozone decomposes significantly faster than in pure water owing to its interaction with H₂O₂. The effective rate constant (k = (0.023 ± 0.002) l/(mol s)) is determined, which is much higher than the overall rate constant of ozone decomposition in water, but much lower than the specific rate of ozone decomposition in water in the presence of common organic admixtures (fulvic acids, ethanol). It is concluded that at the combined use of O₃ and H₂O₂ for the decomposition of organic admixtures in water, the contribution of their interaction with each other is little.     

Pták sum of a Boolean algebra with an effect algebra and its completeness

The aim of the present paper is to show that a bounded Boolean power of an effect algebra has all the analogous properties required for Pták's sum of a Boolean algebra and an orthomodular lattice and to prove a theorem about its completeness. We also give for elements of that Pták sum an important form for their expression.     

Analysis of diffraction efficiency of a holographic coupler with respect to angular divergence

We present a method to optimize the Coupling efficiency between two fibers using a Holographic Coupler taking diffraction effect into account. For this we obtain expressions for field distributions at the end facet of a fiber. The results obtained by using the expression is found to be in good agreement with the finite element method in literature, the small deviation is attributed to the negligence of field in the cladding. We then use the Kogelnik theory to obtain useful formulae suitable for diffracted optical elements. The diffraction efficiency expressions are then used to predict the different parameters of Holograting so as to get maximum diffraction efficiency in a direction where the field distribution from the end facet is minimum thereby increasing the coupling efficiency.      

Stability of a stationary distribution of a master equation with respect to information gain solutions

The asymptotic and complete stabilities of the stationary distribution of a master equation with respect to approximate solutions obtained on the basis of the master equation and the information gain (the Kullback information) were investigated.Work was partially supported by the Polish Ministry of Science, Higher Education and Technology, Project M.R.1.7.