On the ternary complex analysis and its applications

Previouly a possible extension of the complex number, together with its connected trigonometry was introduced. In this paper we focuss on the simplest case of ternary complex numbers. Then, some types of holomorphicity adapted to the ternary complex numbers and the corresponding results upon integration of differential forms are given. Several physical applications are given, and in particuler one type of holomorphic function gives rise to a new form of stationary magnetic field. The movement of a monopole type object in this field is then studied and shown to be integrable. The monopole scattering in the ternary field is finally studied.Comment: LaTeX 28 page

Continuously Crossing u=z in the H3+ Boundary CFT

For AdS boundary conditions, we give a solution of the H3+ two point function involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the full (u,z) unit square. It consists of two patches, one for z<u and one for u<z. Along the u=z "singularity", the solutions from both patches are shown to have finite limits and are merged continuously as suggested by the work of Hosomichi and Ribault. From this two point function, we can derive b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as continuous AdS_2 branes are consistent with our novel shift equations without any new restrictions.Comment: version to appear in JHEP - 12 pages now; sign error with impact on some parts of the interpretation fixed; material added to become more self-contained; role of bulk-boundary OPE in section 4 more carefully discussed; 3 references adde

On hypergeometric series reductions from integral representations, the Kampe de Feriet function, and elsewhere

Single variable hypergeometric functions pFq arise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. For these applications, it is of interest to obtain analytic expressions, and we present the reduction of a number of cases of pFp and p+1F_p, mainly for p=2 and p=3. These and related series have additional applications in quantum and statistical physics and chemistry.Comment: 17 pages, no figure