Related papers: Massless on-shell box integral with arbitrary powe…
We present a new approach to construction of recursion operators for multidimensional integrable systems which have a Lax-type representation in terms of a pair of commuting vector fields. It is illustrated by the examples of the…
Using a Mellin-Barnes representation, we compute the on-shell massless planar double box Feynman diagram with an irreducible scalar product of loop momenta in the numerator. This diagram is needed in calculations of two loop corrections to…
We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
The reflectionless transmission resonances in above-barrier reflection of Bose-Einstein condensates by the Rosen-Morse potential are considered using the mean field Gross-Pitaevskii approach. Applying an exact third order nonlinear…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
One-loop integrands can be written in terms of a simple, process-independent basis. We show that a similar basis exists for integrands of phase-space integrals for the real-emission contribution at next-to-leading order. Our demonstration…
We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like $1\to 3$ decay to Minkowskian regions relevant to all $1\to 3$…
We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive…
Recently, algorithms for calculation of 3-loop propagator diagrams in HQET and on-shell QCD with a heavy quark have been constructed and implemented. These algorithms (based on integration by parts recurrence relations) reduce an arbitrary…
We solve exactly the scalar box integral using the Mellin-Barnes representation. Firstly we recognize the hypergeometric functions resumming the series coming from the scalar integrals, then we perform an analytic continuation before…
We compute the propagator for massless and massive scalar fields in the metric of the pp-wave. The retarded propagator for the massless field is found to stay confined to the surface formed by null geodesics. The algebraic form of the…
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…
We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the ${\mathcal O}(\varepsilon^0)$-part and the ${\mathcal O}(\varepsilon^1)$-part of the sunrise…
We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop propagator-type…
Using the integration by parts method we derive a closed analytical expression for the result of the integration of an arbitrary dimensionally regulated tadpole diagram composed of a massless propagator and two massive ones, each raised…
We construct explicit integral relations between propagators of generalized Schr\"odinger equations that are linked by higher-order supersymmetry. Our results complement and extend the findings obtained in J. Phys.A 40, 10557 (2007) for the…
We proposed a recipe to systematically calculate Feynman integrals containing linear propagators using the auxiliary mass flow method. The key of the recipe is to introduce a quadratic term for each linear propagator and then using…
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these…