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Том 187, № 3 (2016)
- Год: 2016
- Статей: 11
- URL: https://journals.rcsi.science/0040-5779/issue/view/10383
Article
Symmetries of higher-spin current interactions in four dimensions
Аннотация
We show that the current interaction of massless fields in four dimensions breaks the sp(8) symmetry of free massless equations of arbitrary spin down to the conformal symmetry su(2, 2). This breaking agrees with the form of the nonlinear higher-spin field equations.
797-812
Velocity addition and a closed time cycle in Lorentz-noninvariant theories
Аннотация
In theories whose Lorentz invariance is violated by the presence of an external tensor of any rank, we show that a signal velocity, understood as the group velocity of a wave, is added to the velocity of the reference frame according to the standard relativistic rule for adding velocities. In the case where we have a superluminal signal, this observation allows creating a closed time cycle and thus coming to a conclusion about a causality violation even in the absence of relativistic invariance. We also reveal an optical anisotropy of a moving medium that is isotropic at rest.
813-822
Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions
Аннотация
We show that the non-Abelian Hirota difference equation is directly related to a commutator identity on an associative algebra. Evolutions generated by similarity transformations of elements of this algebra lead to a linear difference equation. We develop a special dressing procedure that results in an integrable non-Abelian Hirota difference equation and propose two regular reduction procedures that lead to a set of known equations, Abelian or non-Abelian, and also to some new integrable equations.
823-834
The finite-time blowup of the solution of an initial boundary-value problem for the nonlinear equation of ion sound waves
Аннотация
We obtain blowup conditions for the solutions of initial boundary-value problems for the nonlinear equation of ion sound waves in a hydrogen plasma in the approximation of “hot” electrons and “heavy” ions. A specific characteristic of this nonlinear equation is the noncoercive nonlinearity of the form ∂t|∇u|2, which complicates its study by any energy method. We solve this problem by the Mitidieri–Pohozaev method of nonlinear capacity.
835-841
842-870
Virasoro symmetry of the constrained multicomponent Kadomtsev–Petviashvili hierarchy and its integrable discretization
Аннотация
We construct Virasoro-type additional symmetries of a kind of constrained multicomponent Kadomtsev–Petviashvili (KP) hierarchy and obtain the Virasoro flow equation for the eigenfunctions and adjoint eigenfunctions. We show that the algebraic structure of the Virasoro symmetry is retained under discretization from the constrained multicomponent KP hierarchy to the discrete constrained multicomponent KP hierarchy.
871-887
Equation for one-loop divergences in two dimensions and its application to higher-spin fields
Аннотация
We derive a simple formula for one-loop logarithmic divergences on the background of a two-dimensional curved space–time for theories in which the second variation of the action is a nonminimal second-order operator with small nonminimal terms. In particular, this formula allows calculating terms that are integrals of total derivatives. As an application of the result, we obtain one-loop divergences for higher-spin fields on a constant-curvature background in a nonminimal gauge that depends on two parameters. By an explicit calculation, we demonstrate that with the considered accuracy, the result is gauge independent and, moreover, spin independent for spins s ≥ 3.
888-898
Schwinger–Dyson approach to Liouville field theory
Аннотация
We discuss Liouville field theory in the framework of the Schwinger–Dyson approach and derive a functional equation for the three-point structure constant. We prove the existence of a second Schwinger–Dyson equation based on the duality between the screening charge operators and obtain a second functional equation for the structure constant. We use the system of these two equations to uniquely determine the structure constant.
899-908
A model of nonautonomous dynamics driven by repeated harmonic interaction
Аннотация
We consider an exactly solvable model of nonautonomous W*-dynamics driven by repeated harmonic interaction. The dynamics is Hamiltonian and quasifree. Because of inelastic interaction in the large-time limit, it leads to relaxation of initial states to steady states. We derive the explicit entropy production rate accompanying this relaxation. We also study the evolution of different subsystems to elucidate their eventual correlations and convergence to equilibriums. In conclusion, we prove that the W*-dynamics manifests a universal stationary behavior in a short-time interaction limit.
909-934
Buffering in cyclic gene networks
Аннотация
We consider cyclic chains of unidirectionally coupled delay differential–difference equations that are mathematical models of artificial oscillating gene networks. We establish that the buffering phenomenon is realized in these system for an appropriate choice of the parameters: any given finite number of stable periodic motions of a special type, the so-called traveling waves, coexist.
935-951
Fundamental constants in the theory of two-dimensional uniform spanning trees
Аннотация
Three characteristics of two-dimensional uniform spanning trees are nontrivially related to one another: the average density of a sandpile, the looping constant of a square lattice, and the return probability of a loop-erased random walk. We briefly trace the long history of the discovery of their unexpected rational values.
952-963