Large Scale Analytic Calculations in Quantum Field Theories (Q3387102)

scientific article; zbMATH DE number 7293159

Language	Label	Description	Also known as
English	Large Scale Analytic Calculations in Quantum Field Theories	scientific article; zbMATH DE number 7293159

Statements

instance of

scholarly article

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title

Large Scale Analytic Calculations in Quantum Field Theories (English)

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author

Johannes Blümlein

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published in

Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra

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publication date

12 January 2021

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full work available at URL

https://arxiv.org/abs/1905.02148

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https://bib-pubdb1.desy.de/record/422435

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describes a project that uses

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Harmonic Sums, Polylogarithms,Special Numbers, and Their Generalizations

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Analytic computing methods for precision calculations in quantum field theory

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Automatic Feynman graph generation

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GROUP THEORY FACTORS FOR FEYNMAN DIAGRAMS

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Q5613839

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Applications of algebraic topology. Graphs and networks. The Picard- Lefschetz theory and Feynman integrals

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FEYNMAN GRAPH POLYNOMIALS

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High-precision calculation of multiloop Feynman integrals by difference equations

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Algorithm FIRE-Feynman integral reduction

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\texttt{Reduze} -- Feynman integral reduction in \texttt{C++}

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Complexity estimates for two uncoupling algorithms

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Summation in Finite Terms

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On solutions of linear ordinary difference equations in their coefficient field

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Q3416425

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Solving parameterized linear difference equations in terms of indefinite nested sums and products

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Degree bounds to find polynomial solutions of parameterized linear difference equations in \(\Pi\Sigma\)-fields

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SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS

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Parameterized telescoping proves algebraic independence of sums

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Computer algebra and polynomials. Applications of algebra and number theory

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A refined difference field theory for symbolic summation

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A difference ring theory for symbolic summation

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Summation theory. II: Characterizations of \(R {\Pi}{\Sigma}^{\ast}\)-extensions and algorithmic aspects

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Computer algebra in quantum field theory. Integration, summation and special functions

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An automatized algorithm to compute infrared divergent multi-loop integrals.

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Feynman integral evaluation by a sector decomposition approach (FIESTA)

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SecDec: A general program for sector decomposition

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\texttt{FIESTA 2}: parallelizeable multiloop numerical calculations

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Numerical NLO QCD calculations

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FIESTA4: optimized Feynman integral calculations with GPU support

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Systematic approximation of multi-scale Feynman integrals

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The five-loop beta function for a general gauge group and anomalous dimensions beyond Feynman gauge

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Special values of multiple polylogarithms

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The multiple zeta value data mine

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Q5508372

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Q4103811

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Q4157010

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Multiple Hypergeometric Series: Appell Series and Beyond

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Application of the negative-dimension approach to massless scalar box integrals

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Q3345085

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Transformations of certain hypergeometric functions of three variables

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Massive 3-loop ladder diagrams for quarkonic local operator matrix elements

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Calculating three loop ladder and \(V\)-topologies for massive operator matrix elements by computer algebra

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Q3269298

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Q5393662

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Automatized analytic continuation of Mellin-Barnes integrals

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On the resolution of singularities of multiple Mellin-Barnes integrals

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AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

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The two-mass contribution to the three-loop pure singlet operator matrix element

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Q5820777

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Algebras of Iterated Path Integrals and Fundamental Groups

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Multiple polylogarithms, cyclotomy and modular complexes

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A quasi-finite basis for multi-loop Feynman integrals

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The massless higher-loop two-point function

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Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals

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Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

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Differential equations for two-loop four-point functions.

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Q4234305

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Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations

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An algorithm for solving second order linear homogeneous differential equations

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Automated solution of first order factorizable systems of differential equations in one variable

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Q3732104

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On zero-curvature representations of evolution equations

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Reducing differential equations for multiloop master integrals

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\texttt{epsilon}: a tool to find a canonical basis of master integrals

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Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form

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Algorithmic transformation of multi-loop master integrals to a canonical basis with \textit{CANONICA}

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The 3-loop non-singlet heavy flavor contributions and anomalous dimensions for the structure function \(\mathrm{F}_2(\mathrm{x, Q}^{\mathrm{2}})\) and transversity

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Massive three-loop form factor in the planar limit

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The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates

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The method of arbitrarily large moments to calculate single scale processes in quantum field theory

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MATAD: A program package for the computation of MAssive TADpoles

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Mellin moments of the \(O(\alpha_s^3)\) heavy flavor contributions to unpolarized deep-inelastic scattering at \(Q^{2}\gg m^{2}\) and anomalous dimensions

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The third-order QCD corrections to deep-inelastic scattering by photon exchange

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Ore Polynomials in Sage

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Determining the closed forms of the anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra

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The three-loop splitting functions in QCD: the non-singlet case

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The three-loop splitting functions in QCD: the singlet case

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The three-loop splitting functions \(P_{q g}^{(2)}\) and \(P_{g g}^{(2, \operatorname{N}_{\operatorname{F}})}\)

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The method of differentiating under the integral sign

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Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory

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The elliptic dilogarithm for the sunset graph

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Analytic treatment of the two loop equal mass sunrise graph

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The two-loop sunrise graph with arbitrary masses

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Fourth order spectral functions for the electron propagator

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Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral

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Iterated elliptic and hypergeometric integrals for Feynman diagrams

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Moments of heavy quark correlators with two masses: Exact mass dependence to three loops

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Q4857337

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Q4141415

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Q5790262

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Elliptic surfaces with four singular fibres

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Heun equations coming from geometry

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An elliptic generalization of multiple polylogarithms

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The \(\varepsilon\)-form of the differential equations for Feynman integrals in the elliptic case

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Q5670687

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Modular Forms

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Q4449110

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NEW REPRESENTATIONS FOR APÉRY‐LIKE SEQUENCES

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Feynman integrals and iterated integrals of modular forms

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Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral

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The two-mass contribution to the three-loop gluonic operator matrix element \(A_{g g, Q}^{(3)}\)

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Rationalizing roots: an algorithmic approach

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On integro-differential algebras.

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Iterated binomial sums and their associated iterated integrals

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Quasi-shuffle products

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Algebraic relations between harmonic sums and associated quantities.

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HARMONIC SUMS, MELLIN TRANSFORMS AND INTEGRALS

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Harmonic sums and polylogarithms generated by cyclotomic polynomials

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Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms

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Massive Feynman diagrams and inverse binomial sums

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Expansion around half-integer values, binomial sums, and inverse binomial sums

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Q3134850

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On Nielsen's generalized polylogarithms and their numerical calculation

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Nielsen’s Generalized Polylogarithms

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Q3253375

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Q3916824

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HARMONIC POLYLOGARITHMS

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Nested sums, expansion of transcendental functions, and multiscale multiloop integrals

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Analytic continuation of Mellin transforms up to two-loop order

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Structural relations of harmonic sums and Mellin transforms up to weight \(w=5\)

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Symbolic expansion of transcendental functions

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XSummer -- transcendental functions and symbolic summation in form

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Numerical evaluation of harmonic polylogarithms

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HPL, a Mathematica implementation of the harmonic polylogarithms

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Numerical implementation of harmonic polylogarithms to weight w = 8

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Numerical evaluation of multiple polylogarithms

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A \(K3\) in \(\phi^{4}\)

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Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case

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Unitarity and causality in a renormalizable field theory with unstable particles

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Identifiers

DOI

10.1007/978-3-030-44559-1_5

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:3387102