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Approaches to signal representation and coding theory have traditionally focused on how to best represent signals using parsimonious representations that incur the lowest possible distortion. Classical examples include linear and non-linear…

Information Theory · Computer Science 2015-12-25 Petros T Boufounos , Shantanu Rane , Hassan Mansour

It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…

High Energy Physics - Theory · Physics 2014-04-01 Erik Panzer

The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…

High Energy Physics - Phenomenology · Physics 2023-07-12 O. V. Tarasov

Hermitian symplectic spaces provide a natural framework for the extension theory of symmetric operators. Here we show that hermitian symplectic spaces may also be used to describe the solution to the factorisation problem for the scattering…

Mathematical Physics · Physics 2007-05-23 M. Harmer

The dynamic spectra of pulsars frequently exhibit diverse interference patterns, often associated with parabolic arcs in the Fourier-transformed (secondary) spectra. Our approach differs from previous ones in two ways: first, we extend…

High Energy Astrophysical Phenomena · Physics 2024-05-28 Tobias Kramer , Daniel Waltner , Eric J. Heller , Dan R. Stinebring

In this brief note, we show how to apply Kummer's and other quadratic transformation formulas for Gauss' and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that…

Classical Analysis and ODEs · Mathematics 2019-11-28 Martin Nicholson

We determine the master integrals for vertex and propagator diagrams that appear in effective field theories containing heavy fields. The integrals involve at least one heavy line, and the standard lines include an arbitrary mass scale. The…

High Energy Physics - Phenomenology · Physics 2022-01-19 B. Assi , B. A. Kniehl , A. I. Onishchenko

When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…

High Energy Physics - Theory · Physics 2008-11-26 A. I. Davydychev , M. Yu. Kalmykov

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…

Symbolic Computation · Computer Science 2016-01-11 Jakob Ablinger , Johannes Bluemlein , Abilio de Freitas , Carsten Schneider

We present a short overview over the different contributions to high energy photon photon scattering and explore the possibilities of tuning the sizes of the scattered objects by changing the virtuality of the photons. We compare the…

High Energy Physics - Phenomenology · Physics 2008-11-26 H. G. Dosch

This work presents an approach to improve the precision of polarized photon-photon collisions simulation implemented in the SANCphot package. The basic linear Compton approximation of the incoming photon spectrum is extended to a general…

High Energy Physics - Phenomenology · Physics 2025-12-17 Sergey G. Bondarenko , Aidos Issadykov , Lidia V. Kalinovskaya , Andrey A. Sapronov

A general method to derive the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. In this approach new mathematical objects like non-commuting operators evolving with the Planck constant promoted as a…

Mathematical Physics · Physics 2009-11-10 Pierre Gosselin , Herve Mohrbach

This is the first of two papers in which we study real and virtual photon-proton scattering in a nonperturbative framework. We classify different contributions to this process and identify the leading contributions at high energies. We then…

High Energy Physics - Phenomenology · Physics 2008-11-26 Carlo Ewerz , Otto Nachtmann

We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…

Classical Analysis and ODEs · Mathematics 2018-03-05 Fokko van de Bult , Eric Rains

The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…

Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…

Representation Theory · Mathematics 2015-11-09 Jürgen Fuchs , Christoph Schweigert

We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.

Algebraic Geometry · Mathematics 2007-05-23 J. M. Landsberg , L. Manivel

Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.

Mathematical Physics · Physics 2017-04-05 Giampiero Passarino

We study in detail certain natural continuous representations of G = GL(n,K) in locally convex vector spaces over a locally compact, non-archimedean field K of characteristic zero. We construct boundary value maps, or integral transforms,…

Number Theory · Mathematics 2007-05-23 Peter Schneider , Jeremy Teitelbaum

In this paper we generalize the comparison theorem of Hecht and Taylor to arbitrary parabolic subalgebras of a complex reductive Lie algebra and then apply our generalized comparison theorem to obtain results about the geometric realization…

Representation Theory · Mathematics 2008-04-03 Tim Bratten