Particles in a Singular Asymptotic Limit of a Classical Field Theory

We give a detailed discussion of the singular asymptotic limit of a classical field theory as a small parameter goes to zero. The phenomenon under investigation is the appearance of particles in the limit. The particles are rescaled kinks of a sine-Gordon field acted on by a second field. As the parameter goes to zero, these kinks shrink while their energy is invariant, leaving point-like particles accelerated by the second field. The validity of this picture of the asymptotics hinges on the dispersive nature of the radiative correction to the kink produced by the perturbation. This is analysed using a perturbation theory based on complete integrability.     

Existence and Nonexistence of Global Classical Solutions to Porous Medium and Plasma Equations with Singular Sources

Let Ω be a bounded or unbounded domain in R^n. The initial-boundary value problem for the porous medium and plasma equation with singular terms is considered in this paper. Criteria for the appearance of quenching phenomenon and the existence of global classical solution to the above problem are established. Also, the life span of the quenching solution is estimated or evaluated for some domains.     

Rational Conformal Field Theory in Four Dimensions

We use the recently established rationality of correlation functions in a globally conformally invariant quantum field theory satisfying Wightman axioms to construct a family of solvable models in the four-dimensional Minkowski space–time. We consider the model of a neutral two-dimension scalar field in detail. It depends on a positive real parameter c, an analogue of the Virasoro central charge; for all (finite) c, it admits an infinite number of conserved symmetric tensor currents. The operator product algebra of coincides with a simpler one generated by a bilocal scalar field V(x ₁,x ₂) of dimension 1+1. The modes of V together with the unit operator span an infinite-dimensional Lie algebra _V , whose vacuum (i.e., zero-energy lowest-weight) representations depend only on the central charge c. The Wightman positivity (i.e., unitarity of the representations of _V ) is proved equivalent to c.     

Toward an Infinite-Component Field Theory with a Double Symmetry: Interaction of Fields

We complete the first stage of constructing a theory of fields not investigated before; these fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible representations. We consider only those theories that initially have a double symmetry: relativistic invariance and the invariance under the transformations of a secondary symmetry generated by the polar or the axial four-vector representation of the orthochronous Lorentz group. The high symmetry of the theory results in an infinite degeneracy of the particle mass spectrum with respect to spin. To eliminate this degeneracy, we postulate a spontaneous secondary-symmetry breaking and then solve the problems on the existence and the structure of nontrivial interaction Lagrangians.     

Massless Elementary Particles in a Quantum Theory over a Galois Field

We consider massless elementary particles in a quantum theory based on a Galois field (GFQT). We previously showed that the theory has a new symmetry between particles and antiparticles, which has no analogue in the standard approach. We now prove that the symmetry is compatible with all operators describing massless particles. Consequently, massless elementary particles can have only half-integer spin (in conventional units), and the existence of massless neutral elementary particles is incompatible with the spin–statistics theorem. In particular, this implies that the photon and the graviton in the GFQT can only be composite particles.     

Polarization of the Electron–Positron Vacuum by a Strong Magnetic Field in the Theory with a Fundamental Mass

In the framework of the theory with a fundamental mass in the one-loop approximation, we evaluate the exact Lagrange function of the strong constant magnetic field, replacing the Heisenberg–Euler Lagrangian in the traditional QED. We establish that the derived generalization of the Lagrange function is real for arbitrary values of the magnetic field. In the weak field, the evaluated Lagrangian coincides with the known Heisenberg–Euler formula. In extremely strong fields, the field dependence of the Lagrangian completely disappears; in this range, the Lagrangian tends to the limit value determined by the ratio of the fundamental and lepton masses.     

Equation for the Complex Energy of a Bound Particle in a Laser Radiation Field in the Presence of Strong Constant Electromagnetic Fields

We construct exact solutions of the Schrodinger and Pauli equations for charged particles in the external field of the Redmond generalized configuration. We calculate the Green's functions of scalar and spinning particles in this field. Using them, we calculate the equations for the complex quasienergy of a bound particle (bound by a short-range potential) two different ways. In the example of an external constant electric field, we discuss the applicability domain of the obtained equations and the differences between their solutions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 198–211, November, 2005.     

Scattering Problem for a Classical Particle with Spin in a Coulomb Field

We investigate the scattering problem for a relativistic electron with spin in a Coulomb field in the framework of pseudoclassical mechanics. We obtain an analytic expression for the scattering angle and limiting estimates for the scattering parameters for the spinless and nonrelativistic cases. For small angles, the pseudoclassical model under consideration leads to the well-known quantum-mechanical Mott formula.     

一个具有电荷和磁偶极矩黑洞的量子非热辐射及其辐射粒子射程的特征

一个稳态轴对称非Kerr-Newman黑洞时空中的粒子能级分布与电磁四维势有关，黑洞电荷和磁偶极矩的存在以及裸奇点的出现都对粒子能级分布有影响，粒子能级分布与方向有关.此黑洞的量子非热辐射及其粒子的平均射程与辐射粒子的能量范围有关。     

磁场和热辐射对可变表面热通量作用下的竖直圆锥体自然对流的影响

就圆锥体表面受到可变表面热通量作用,计及磁场和热辐射的综合影响,数值研究了流经竖直圆锥体的自然对流及其热交换特点.认为流体是灰色的、吸收-发射的辐射介质,而非散射介质,通过近似变换,将自由对流区中流动的边界层控制方程,简化为无量纲方程.利用Crank-Nicol-son形式的隐式有限差分法(具有收敛快、精度高、无条件稳定的特点),求解了无量纲的控制方程.得到了数值结果,以及空气和水中的速度、温度、局部和平均的壁面剪应力、局部和平均的Nusselt数.将所得到的结果与先前文献报道的结果进行比较,发现两者有着很好的一致性.     

Singular quasilinear equations with quadratic growth in the gradient without sign condition

Given a bounded domain Ω in RN, and a function a∈Lq(Ω) with q>N/2, we study the existence of a positive solution for the quasilinear problem

     

Control of Affine Nonlinear Systems with Nilpotent Structure in Singular Problems

The minimum singular functional control problem is analyzed for a class of multi-input affine nonlinear systems under the hypothesis that the associated Lie algebra is nilpotent. The optimal control corresponding to the first, second, and third order nilpotent operators is determined. We develop an algorithm for solving the singular problem that is applicable whether or not singular subarcs exist in the optimal control.This work was partial supported by the Romanian Aerospace Agency, Grant 31032.     

The Gravitational Field of an Electrically Charged Mass Point and the Causality Principle in the RTG

We find the effective Riemannian space–time corresponding to the gravitational field generated by a charged mass point in the framework of the relativistic theory of gravity. The causality principle plays an important role in solving this problem. The analytic form and the domain of definition, i.e., the gravitational radius, of the obtained solution differ from the corresponding results in Einstein's general relativity theory.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Time delay in scattering by potentials and by magnetic fields with two supports at large separation

We study the asymptotic behavior of the time delay (defined as the trace of the Eisenbud-Wigner time delay operator) for scattering by potential and by magnetic field with two compact supports as the separation of supports goes to infinity. The emphasis is placed on analyzing how different the asymptotic formulae are in potential and magnetic scattering. The difference is proper to scattering in two dimensions.     

Singular homogenization with stationary in time and periodic in space coefficients

We study the homogenization problem for a random parabolic operator with coefficients rapidly oscillating in both the space and time variables and with a large highly oscillating nonlinear potential, in a general stationary and mixing random media, which is periodic in space. It is shown that a solution of the corresponding Cauchy problem converges in law to a solution of a limit stochastic PDE.