v 1 9 A ug 1 99 6 Axially Symmetric

ar X iv : q - a lg / 9 60 80 20 v 1 2 3 A ug 1 99 6 SHIFTED JACK POLYNOMIALS , BINOMIAL FORMULA , AND APPLICATIONS

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [

v 1 2 2 N ov 1 99 6 General Static Axially - symmetric Solutions of ( 2 + 1 ) - dimensional Einstein - Maxwell - Dilaton

We obtain the general static solutions of the axially symmetric (2+1)dimensional Einstein-Maxwell-Dilaton theory by dimensionally reducing it to a 2-dimensional dilaton gravity theory. The solutions consist of the magnetically charged sector and the electrically charged sector. We illuminate the relationship between the two sectors by pointing out the transformations between them. 04.20.jb, 04....

/ 95 08 35 6 v 1 2 3 A ug 1 99 5 MC / TH 95 / 14 ρ → 4 π in chirally symmetric models

0 v 1 1 2 A ug 1 99 6 Vacuum energy in a spherically symmetric background field

The vacuum energy of a scalar field in a spherically symmetric background field is considered. It is expressed through the Jost function of the corresponding scattering problem. The renormalization is discussed in detail and performed using the uniform asymptotic expansion of the Jost function. The method is demonstrated in an simple explicit example.

X iv : a st ro - p h / 99 08 06 9 v 1 6 A ug 1 99 9 ISO observations of the BL Lac object PKS 2155 – 304