Some comments on the divergence of perturbation series in Quantum Eletrodynamics

It has been argued by Dyson that the perturbation series in coupling constant in QED can not be convergent. We find that similiar albeit slightly different arguments lead to the divergence of the series of $1/N_f$ expansion in QED.Comment: Final Version, To appear in Modern Physics Letters

Relation between spectral changes and the presence of the lower kHz QPO in the neutron-star low-mass X-ray binary 4U 1636-53

We fitted the $3-180$-keV spectrum of all the observations of the neutron-star low-mass X-ray binary 4U 1636$-$53 taken with the {\it Rossi X-ray Timing Explorer} using a model that includes a thermal Comptonisation component. We found that in the low-hard state the power-law index of this component, $\Gamma$, gradually increases as the source moves in the colour-colour diagram. When the source undergoes a transition from the hard to the soft state $\Gamma$ drops abruptly; once the source is in the soft state $\Gamma$ increases again and then decreases gradually as the source spectrum softens further. The changes in $\Gamma$, together with changes of the electron temperature, reflect changes of the optical depth in the corona. The lower kilohertz quasi-periodic oscillation (kHz QPO) in this source appears only in observations during the transition from the hard to the soft state, when the optical depth of the corona is high and changes depends strongly upon the position of the source in the colour-colour diagram. Our results are consistent with a scenario in which the lower kHz QPO reflects a global mode in the system that results from the resonance between, the disc and/or the neutron-star surface, and the Comptonising corona.Comment: 9 pages, 6 figures. Accepted for publication in MNRA

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case

We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field $O(k)$ and the regularization .Comment: minor correction

Recursion relations and branching rules for simple Lie algebras

The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights $\Gamma$ specific for each injection. The structure of $\Gamma$ is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for $A_{3} \oplus u(1) \to B_{4}$ injection.Comment: 15p.,LaTe

On the relation between p-adic and ordinary strings

The amplitudes for the tree-level scattering of the open string tachyons, generalised to the field of p-adic numbers, define the p-adic string theory. There is empirical evidence of its relation to the ordinary string theory in the p_to_1 limit. We revisit this limit from a worldsheet perspective and argue that it is naturally thought of as a continuum limit in the sense of the renormalisation group.Comment: 13 pages harvmac (b), 2 eps figures; v2: revtex, shortened, published versio

Fermi Detection of the Pulsar Wind Nebula HESS J1640-465

We present observations of HESS J1640-465 with the Fermi-LAT. The source is detected with high confidence as an emitter of high-energy gamma-rays. The spectrum lacks any evidence for the characteristic cutoff associated with emission from pulsars, indicating that the emission arises primarily from the pulsar wind nebula. Broadband modeling implies an evolved nebula with a low magnetic field resulting in a high gamma-ray to X-ray flux ratio. The Fermi emission exceeds predictions of the broadband model, and has a steeper spectrum, possibly resulting from a distinct excess of low energy electrons similar to what is inferred for both the Vela X and Crab pulsar wind nebulae.Comment: 6 pages, 5 figures, accepted for publication in Ap

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator

A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential.Comment: 6 pages, 8 eps figure