17,570 research outputs found
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams
It is shown how strictly four-dimensional integration by parts combined with
differential renormalization and its infrared analogue can be applied for
calculation of Feynman diagrams.Comment: 6 pages, late
Small-threshold behaviour of two-loop self-energy diagrams: two-particle thresholds
The behaviour of two-loop two-point diagrams at non-zero thresholds
corresponding to two-particle cuts is analyzed. The masses involved in a cut
and the external momentum are assumed to be small as compared to some of the
other masses of the diagram. By employing general formulae of asymptotic
expansions of Feynman diagrams in momenta and masses, we construct an algorithm
to derive analytic approximations to the diagrams. In such a way, we calculate
several first coefficients of the expansion. Since no conditions on relative
values of the small masses and the external momentum are imposed, the threshold
irregularities are described analytically. Numerical examples, using diagrams
occurring in the Standard Model, illustrate the convergence of the expansion
below the first large threshold.Comment: 28 pages (including 23 pages of text in latex and 5 pages with 6
figures in a separate postcript file
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