A5030657938- Black Holes and Theoretical Physics
- Particle physics theoretical and experimental studies
- Algebraic and Geometric Analysis
- Advanced Mathematical Identities
- Analytic Number Theory Research
- Cosmology and Gravitation Theories
- Mathematics and Applications
- Polynomial and algebraic computation
- Algebraic Geometry and Number Theory
- Advanced Algebra and Geometry
- Noncommutative and Quantum Gravity Theories
- Advanced Differential Equations and Dynamical Systems
- advanced mathematical theories
- Quantum Chromodynamics and Particle Interactions
- Semiconductor materials and devices
- Education Methods and Technologies
- Advanced Combinatorial Mathematics
- Advancements in Semiconductor Devices and Circuit Design
- Mathematical functions and polynomials
- Integrated Circuits and Semiconductor Failure Analysis
- Distributed and Parallel Computing Systems
- Sociology and Education Studies
- High-Energy Particle Collisions Research
- Particle Detector Development and Performance
- Cryptography and Residue Arithmetic
Infineon Technologies (Germany)
2022-2023
TU Wien
2023
Humboldt-Universität zu Berlin
2013-2020
Johannes Gutenberg University Mainz
2007-2020
Max Planck Society
2019
Max Planck Institute for Physics
2018
Michigan State University
2018
UCLouvain
2018
University of Oxford
2018
European Organization for Nuclear Research
2018
We present the two-loop sunrise integral with arbitrary non-zero masses in two space-time dimensions terms of elliptic dilogarithms. find that structure result is as simple and elegant equal mass case, only arguments dilogarithms are modified. These have a nice geometric interpretation.
We present the result for finite part of two-loop sunrise integral with unequal masses in four space-time dimensions terms O(ε0)-part and O(ε1)-part around two dimensions. The latter integrals are given elliptic generalisations Clausen Glaisher functions. Interesting aspects occurrence depth objects weights individual terms.
The integrand of any multiloop integral is characterized after Feynman parametrization by two polynomials. In this review we summarize the properties these Topics covered in paper include among others: spanning trees and forests, all-minors matrix-tree theorem, recursion relations due to contraction deletion edges, Dodgson's identity matroids.
We present a method to compute the Laurent expansion of two-loop sunrise integral with equal non-zero masses arbitrary order in dimensional regularisation ε. This is done by introducing class functions (generalisations multiple polylogarithms include elliptic case) and showing that all integrations can be carried out within this functions.
We discuss the analytical solution of two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The result is obtained by solving a second-order differential equation. involves elliptic integrals and particular solutions corresponding homogeneous equation are given periods an curve.
We show that the Laurent series of two-loop kite integral in D = 4 − 2ε space-time dimensions can be expressed each order expansion terms elliptic generalisations (multiple) polylogarithms. Using differential equations, we present an iterative method to compute any desired order. As example, give first three orders explicitly.
We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain momentum space IBP relations, which are well-known in physics literature. Applying a result of Loeser and Sabbah, we conclude that number master is computed by Euler characteristic Lee-Pomeransky polynomial. illustrate techniques to compute this various examples compare it with numbers obtained previous works.
We solve the two-loop sunrise integral with unequal masses systematically to all orders in dimensional regularisation parameter $\varepsilon$. In order do so, we transform system of differential equations for master integrals an $\varepsilon$-form. The depends on three kinematical variables. perform a change variables standard coordinates moduli space ${\mathcal M}_{1,3}$ genus one Riemann surface marked points. This gives us solution as iterated $\overline{\mathcal M}_{1,3}$. On...
We study the analytic continuation of Feynman integrals from kite family, expressed in terms elliptic generalisations (multiple) polylogarithms. Expressed this way, are functions two periods an curve. show that all what is required just these periods. present explicit formula for values t∈R. Furthermore, nome q curve satisfies over complete range t inequality |q|≤1, where |q|=1 attained only at singular points t∈{m2,9m2,∞}. This ensures convergence q-series expansion ELi-functions and...
We consider multiloop integrals in dimensional regularization and the corresponding Laurent series. study integral Euclidean region where all ratios of invariants masses have rational values. prove that this case coefficients series are periods.
This paper describes algorithms for the exact symbolic computation of period integrals on moduli spaces M 0,n curves genus 0 with n ordered marked points, and applications to Feynman integrals.
Institut des Hautes Etudes ScientifiquesLe Bois-Marie 35, route de Chartres, 91440 Bures-sur-Yvette, FranceE-mail:bogner@math.hu-berlin.de, brown@math.jussieu.frWe review a method for the algebraic treatment of family functions which contains mul-tiple polylogarithms, with applications to symbolic calculation Feynman integrals.Loops and Legs in Quantum Field Theory - 11th DESY Workshop onElementary Particle Physics,April 15-20, 2012Wernigerode, Germany
Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic as well results made available by the community. Its bibliometry complementary that of SPIRES or arXiv in sense it admits searching integrals graph-theoretical objects, e.g. its topology.
The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates 100 TeV proton-proton collider. It offers vast new domain of exploration particle physics, orders magnitude advances terms Precision, Sensitivity and Energy. implementation plan foresees, as first step, an Electroweak Factory electron-positron This high luminosity facility, operating between 90 365 GeV centre-of-mass energy, will study the heavy particles Standard...
We present the result for finite part of two-loop sunrise integral with unequal masses in four space-time dimensions terms ${\mathcal O}(\varepsilon^0)$-part and O}(\varepsilon^1)$-part around two dimensions. The latter integrals are given elliptic generalisations Clausen Glaisher functions. Interesting aspects occurrence depth objects weights individual terms.