arXiv subjects

G. A. Sarkissian

Publications and source records attributed to G. A. Sarkissian.

7 recordsLinked to original sources

arXiv2026

From hyperbolic to complex Euler integrals

Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional integrals over the complex plane.

math.CA↗

arXiv2025

Complex binomial theorem and pentagon identities

We consider different pentagon identities realized by the hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields the complex binomial theorem which coincides with the Fourier transformation of the complex analogue of the Euler beta integral. At the bottom we obtain a Fourier transformation formula for the complex gamma function. This is done with the help of a new type of the limit $ω_1+ω_2\to 0$ (or $b\to \textrm{i}$ in two-dimensional conformal field theory) applied to the hyperbolic hypergeometric integrals.

math.CA↗

arXiv2025

Complex rational Ruijsenaars model. The two-particle case

We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit $ω_1+ω_2\to 0$ (or $b\to \imath$ in $2d$ CFT) and investigate in detail the two-particle case. Corresponding wave functions are described by complex hypergeometric functions in the Mellin-Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter $Q$-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special $ω_1-ω_2\to 0$ (or $b\to 1$) limit. Additionally, two new degenerations to the complex Calogero-Sutherland type models are described.

math-ph↗

arXiv2024

Complex and rational hypergeometric functions on root systems

We consider some new limits for the elliptic hypergeometric integrals on root systems. After the degeneration of elliptic beta integrals of type I and type II for root systems $A_n$ and $C_n$ to the hyperbolic hypergeometric integrals, we apply the limit $ω_1\to - ω_2$ for their quasiperiods (corresponding to $b\to i$ in the two-dimensional conformal field theory) and obtain complex beta integrals in the Mellin--Barnes representation admitting exact evaluation. Considering type I elliptic hypergeometric integrals of a higher order obeying nontrivial symmetry transformations, we derive their descendants to the level of complex hypergeometric functions and prove the Derkachov--Manashov conjectures for functions emerging in the theory of non-compact spin chains. We describe also symmetry transformations for a type II complex hypergeometric function on the $C_n$-root system related to the recently derived generalized complex Selberg integral. For some hyperbolic beta integrals we consider a special limit $ω_1\to ω_2$ (or $b\to 1$) and obtain new hypergeometric identities for sums of integrals of rational functions.

math.CA↗

arXiv2022

Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group

We show that the complex hypergeometric function describing $6j$-symbols for $SL(2,\mathbb{C})$ group is a special degeneration of the $V$-function -- an elliptic analogue of the Euler-Gauss $_2F_1$ hypergeometric function. For this function, we derive mixed difference-recurrence relations as limiting forms of the elliptic hypergeometric equation and some symmetry transformations. At the intermediate steps of computations, there emerge a function describing the $6j$-symbols for the Faddeev modular double and the corresponding difference equations and symmetry transformations.

math-ph↗

arXiv2022

Complex hypergeometric functions and integrable many-body problems

General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable $N$-body systems emerging from particular degenerations of the elliptic Ruijsenaars and van Diejen models.

math-ph↗

arXiv1994

Pseudoclassical and quantum theory of the D=2n dimensional relativistic spinning particle with anomalous "magnetic" moment in the external Yang-Mills field

The pseudoclassical hamiltonian and action of the $D=2n$ dimensional Dirac particle with anomalous magnetic moment interacting with the external Yang-Mills field are found. The Bargmann-Michel-Telegdi equation of motion for the Pauli-Lubanski vector is deduced. The canonical quantization of $D=2n$ dimensional Dirac spinning particle with anomalous magnetic moment in the external Yang-Mills field is carried out in the gauge which allows to describe simultaneously particles and antiparticles (massive and massless) already at the classical level. Pseudoclassical Foldy-Wouthuysen transformation is used to obtain canonical (Newton-Wigner) coordinates and in terms of these variables the theory is quantized.

hep-th↗