Arbitrary Four String Scattering at High Energy and Fixed Angle

We calculate, using the group theoretic approach to string theory, the tree and one loop scattering of four open and closed arbitrary bosonic string states. In the limit of high energy, but fixed angle, the multi-string vertex at tree and one loop levels that we find takes a very simple form. We propose, and present arguments for, a form for the high energy multi-string vertex at all loops; in particular we give a path integral derivation of this vertex. Our results agree with those of Gross and Mende for tachyon scattering amplitudes, but those for any other string scattering are substantially different from that discussed in reference [5]. We also develop some of the technology used in the group theoretic method to compute loop corrections.Comment: Plain tex, 55 pages, 2 figures. A new section is added, giving a path integral derivation of four arbitrary string high energy scattering, in agreement with the results given earlier. Typos corrected, and some discussion in section 7 clarifie

Convergent sequences of perturbative approximations for the anharmonic oscillator II. Compact time approach

We present an alternative pathway in the application of the variation improvement of ordinary perturbation theory exposed in [1] which can preserve the internal symmetries of a model by means of a time compactification.Comment: 21 pages, 4 Postscript figures available through anonymous ftp at ftp://algol.lpm.univ-montp2.fr ; replaces version which could not be postscripted presumably for lack of figures.uu fil

Angpow: a software for the fast computation of accurate tomographic power spectra

The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular the matter power spectrum $P(k)$ brings information about the cosmological distance evolution and the galaxy clustering together. However the building of $P(k)$ from galaxy catalogues needs a cosmological model to convert angles on the sky and redshifts into distances, which leads to difficulties when comparing data with predicted $P(k)$ from other cosmological models, and for photometric surveys like LSST. The angular power spectrum $C_\ell(z_1,z_2)$ between two bins located at redshift $z_1$ and $z_2$ contains the same information than the matter power spectrum, is free from any cosmological assumption, but the prediction of $C_\ell(z_1,z_2)$ from $P(k)$ is a costly computation when performed exactly. The Angpow software aims at computing quickly and accurately the auto ($z_1=z_2$) and cross ($z_1 \neq z_2$) angular power spectra between redshift bins. We describe the developed algorithm, based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. We validate the results with other codes, and benchmark the performance. Angpow is flexible and can handle any user defined power spectra, transfer functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the $C_\ell(z_1,z_2)$ comparison with data. We emphasize that the Limber's approximation, often used to fasten the computation, gives wrong $C_\ell$ values for cross-correlations.Comment: Published in Astronomy & Astrophysic

Square summability of variations and convergence of the transfer operator

In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in [7]. We also prove uniqueness of so-called G-measures, introduced by Brown and Dooley [2], under square summability of variations.Comment: 8 page

Convergent sequences of perturbative approximations for the anharmonic oscillator I. Harmonic approach

We present numerical evidence that a simple variational improvement of the ordinary perturbation theory of the quantum anharmonic oscillator can give a convergent sequence of approximations even in the extreme strong coupling limit, the purely anharmonic case. Some of the new techniques of this paper can be extended to renormalizable field theories.Comment: 29 pages, 12 Postscript figures available through anonymous ftp at ftp://algol.lpm.univ-montp2.fr ; replaces earlier version which could not be postscripted presumably due to lack of figures.uu fil