Flat wormholes from straight cosmic strings

Special multi-cosmic string metrics are analytically extended to describe configurations of Wheeler-Misner wormholes and ordinary cosmic strings. I investigate in detail the case of flat, asymptotically Minkowskian, Wheeler-Misner wormhole spacetimes generated by two cosmic strings, each with tension $-1/4G$.Comment: 5 pages, latex, no figure

Breathing Relativistic Rotators and Fundamental Dynamical Systems

Recently, it was shown, that the mechanical model of a massive spinning particle proposed by Kuzenko, Lyakhovich and Segal in 1994, which is also the fundamental relativistic rotator rediscovered independently 15 years later by Staruszkiewicz in quite a different context, is defective as a dynamical system, that is, its Cauchy problem is not well posed. This dynamical system is fundamental, since its mass and spin are parameters, not arbitrary constants of motion, which is a classical counterpart of quantum irreducibility. It is therefore desirable to find other objects which, apart from being fundamental, would also have well posed Cauchy problem. For that purpose, a class of breathing rotators is considered. A breathing rotator consists of a single null vector associated with position and moves in accordance with some relativistic laws of motion. Surprisingly, breathing rotators which are fundamental, are also defective as dynamical systems. More generally, it has been shown, that the necessary condition for a breathing rotator to be similarly defective, is functional dependence of its Casimir invariants of the Poincar{\'e} group

Infrared limit in external field scattering

Scattering of electrons/positrons by external classical electromagnetic wave packet is considered in infrared limit. In this limit the scattering operator exists and produces physical effects, although the scattering cross-section is trivial.Comment: 12 pages; published version; minor corrections; comments adde

Spinor particle. An indeterminacy in the motion of relativistic dynamical systems with separately fixed mass and spin

We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite worldline). This paradox suggests that for a consistent description of spinning particles something more general than a worldline concept should be used. As a particular case, we study at the Lagrangian level the Cauchy problem for a spinor particle and then, at the constrained Hamiltonian level, we generalize our result to other particles.Comment: 10 pages, 1 figur

Covariant EBK quantization of the electromagnetic two-body problem

We discuss a method to transform the covariant Fokker action into an implicit two-degree-of-freedom Hamiltonian for the electromagnetic two-body problem with arbitrary masses. This dynamical system appeared 100 years ago and it was popularized in the 1940's by the still incomplete Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. The Hamiltonian formalism is then used to motivate an EBK quantization based on the classical trajectories with a non-perturbative formula that predicts energies free of infinities.Comment: 21 page

Stiff Stability of the Hydrogen atom in dissipative Fokker electrodynamics

We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) timescale into the dynamics. As an application, we study the phenomenon of resonant dissipation, i.e., a motion where both particles recoil together in a drifting circular orbit (a bound state), while the atom dissipates center-of-mass energy only. This balancing of the stiff dynamics is established by the existence of a quartic resonant constant that locks the dynamics to the neighborhood of the recoiling circular orbit. The resonance condition quantizes the angular momenta in reasonable agreement with the Bohr atom. The principal result is that the emission lines of quantum electrodynamics (QED) agree with the prediction of our resonance condition within one percent average deviation.Comment: 1 figure, Notice that Eq. (34) of the Phys. Rev. E paper has a typo; it is missing the square Brackets of eq. (33), find here the correct e

On the structure of the supplementary series of unitary irreducible representations of the proper, ortochronous Lorentz group

Representations from the supplementary series of unitary irreducible representations of the proper, ortochronous Lorentz group are labelled by the parameter z , 0 < z < 1 . There are qualitative differences between representations with 0 < z < 1/2 and those with 1/2 < z < 1 . Two such differences are described in this paper: the probability density of parabolic rotations in a spherically symmetric state is singular at the origin for 0 < z < 1/2 but regular for 1/2 < z < 1 ; the Casimir operator of the little group, which preserves a space-like vector, has for 0 < z < 1/2 a bound state which disappears for 1/2 < z < 1.Зображення з додаткової серії унітарних незвідних зображень власної ортохронної групи Лоренца характеризуються параметром z , 0 < z < 1 . Існують якісні відмінності між зображеннями із 0 < z < 1 та із 1/2 < z < 1 . Дві такі відмінності описано у статті: густина ймовірности параболічних поворотів у сферично-симетричному стані синґулярна в початку координат для 0 < z < 1 , але реґулярна для 1/2 < z < 1 ; оператор Казимира малої групи, яка зберігає просторово-подібний вектор, має для 0 < z < 1 зв’язаний стан, який зникає, коли 1/2 < z < 1

The regular cosmic string in Born-Infeld gravity

It is shown that Born-Infeld gravity --a high energy deformation of Einstein gravity-- removes the singularities of a cosmic string. The respective vacuum solution results to be free of conical singularity and closed timelike curves. The space ends at a minimal circle where the curvature invariants vanish; but this circle cannot be reached in a finite proper time.Comment: 4 pages, submitted to Proceedings of Spanish Relativity Meeting 2010 (ERE2010, Granada, Spain