Solving the characteristic initial value problem for colliding plane gravitational and electromagnetic waves

A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method generalizes the monodromy transform approach to fields with nonanalytic behaviour on the characteristics inherent to waves with distinct wave fronts. The crux of the method is in a reformulation of the main nonlinear symmetry reduced field equations as linear integral equations whose solutions are determined by generalized (``dynamical'') monodromy data which evolve from data specified on the initial characteristics (the wavefronts).Comment: 4 pages, RevTe

Second bound state of PsH

The existence of a second bound state of PsH that is electronically stable and also stable against positron annihilation by the normal 2gamma and 3gamma processes is demonstrated by explicit calculation. The state can be found in the 2,4So symmetries with the two electrons in a spin triplet state. The binding energy against dissociation into the H(2p) + Ps(2p) channel was 6.06x10-4 Hartree. The dominant decay mode of the states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation. The NaPs system of the same symmetry is also electronically stable with a binding energy of 1.553x10-3 Hartree with respect to the Na(3p) + Ps(2p) channel.Comment: 4 pages, 2 figures, RevTex styl

Collision of plane gravitational and electromagnetic waves in a Minkowski background: solution of the characteristic initial value problem

We consider the collisions of plane gravitational and electromagnetic waves with distinct wavefronts and of arbitrary polarizations in a Minkowski background. We first present a new, completely geometric formulation of the characteristic initial value problem for solutions in the wave interaction region for which initial data are those associated with the approaching waves. We present also a general approach to the solution of this problem which enables us in principle to construct solutions in terms of the specified initial data. This is achieved by re-formulating the nonlinear dynamical equations for waves in terms of an associated linear problem on the spectral plane. A system of linear integral ``evolution'' equations which solve this spectral problem for specified initial data is constructed. It is then demonstrated explicitly how various colliding plane wave space-times can be constructed from given characteristic initial data.Comment: 33 pages, 3 figures, LaTeX. Accepted for publication in Classical and Quantum Gravit

Integrability of generalized (matrix) Ernst equations in string theory

The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d\times d$-matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion for a truncated bosonic parts of the low-energy effective action respectively for a dilaton and $d\times d$ - matrix of moduli fields or for a string gravity model with a scalar (dilaton) field, U(1) gauge vector field and an antisymmetric 3-form field, all depending on two space-time coordinates only. We construct the corresponding spectral problems based on the overdetermined $2d\times 2d$-linear systems with a spectral parameter and the universal (i.e. solution independent) structures of the canonical Jordan forms of their matrix coefficients. The additionally imposed conditions of existence for each of these systems of two matrix integrals with appropriate symmetries provide a specific (coset) structures of the related matrix variables. An equivalence of these spectral problems to the original field equations is proved and some approach for construction of multiparametric families of their solutions is envisaged.Comment: 15 pages, no figures, LaTeX; based on the talk given at the Workshop ``Nonlinear Physics: Theory and Experiment. III'', 24 June - 3 July 2004, Gallipoli (Lecce), Italy. Minor typos, language and references corrections. To be published in the proceedings in Theor. Math. Phy

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

Various versions of analytic QCD and skeleton-motivated evaluation of observables

We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the ``minimal'' analytic QCD and which reproduce the measured value of the semihadronic tau decay ratio r{tau}. Further, we describe an approach of calculating the higher order analytic couplings Ak (k=2,3,...) on the basis of logarithmic derivatives of the analytic coupling A1(Q^2). This approach can be easily applied in any version of analytic QCD. We adjust the free parameters of the afore-mentioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of r{tau} and of the Bjorken polarized sum rule (BjPSR) db(Q^2) at a given point (e.g., at Q^2=2 GeV^2). We then evaluate the low-energy behavior of the Adler function dv(Q^2) and the BjPSR db(Q^2) in the afore-mentioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the ``minimal'' analytic QCD and with the evaluation approach of Milton et al. and Shirkov.Comment: 30 pages, 14 eps-figures; v3: parameters of the analytic QCD models M1 and M2 were refined, the numerical results modified accordingly, new paragraph at the end of Sec.II and at the end of Sec.III, discussion of Figs.4 extended, references added; version to appear in PR

Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons

Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schroedinger equation. Here we begin important tests of the relativistic sixteen component wave function solutions obtained in a recent work on meson spectroscopy, extending a method developed previously for positronium decay into two photons. Preliminary to this we examine the positronium decay in the 3P_{0,2} states as well as the 1S_0. The two-gamma quarkonium decays that we investigate are for the \eta_{c}, \eta_{c}^{\prime}, \chi_{c0}, \chi_{c2}, \pi^{0}, \pi_{2}, a_{2}, and f_{2}^{\prime} mesons. Our results for the four charmonium states compare well with those from other quark models and show the particular importance of including all components of the wave function as well as strong and CM energy dependent potential effects on the norm and amplitude. The results for the \pi^{0}, although off the experimental rate by 15%, is much closer than the usual expectations from a potential model. We conclude that the Two-Body Dirac equations lead to wave functions which provide good descriptions of the two-gamma decay amplitude and can be used with some confidence for other purposes.Comment: 79 pages, included new sections on covariant scalar product and added pages on positronium decay for 3P0 and 3P_2 state