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020 _a9783030802196
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024 7 _a10.1007/978-3-030-80219-6
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082 0 4 _a530.15
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245 1 0 _aAnti-Differentiation and the Calculation of Feynman Amplitudes
_h[electronic resource] /
_cedited by Johannes Blümlein, Carsten Schneider.
250 _a1st ed. 2021.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2021.
300 _aXIII, 545 p. 79 illus., 31 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
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490 1 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x2197-8409
505 0 _aGraph complexes and Cutkosky rules -- Differential equations and dispersion relations for Feynman amplitudes with elliptic functions -- Elliptic integrals and the two-loop ttbar production in QCD -- Solutions of 2nd and 3rd order differential equations with more singularities -- Analytic continuation of Feynman diagrams with elliptic solutions -- Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes -- Genus one superstring amplitudes and modular forms -- Difference field methods in Feynman diagram calculations -- Feynman integrals and iterated integrals of modular forms -- Iterated elliptic and hypergeometric integrals for Feynman diagrams. - Feynman integrals, L-series and Kloosterman moments.
520 _aThis volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
650 0 _aMathematical physics.
650 0 _aComputer science
_xMathematics.
650 1 4 _aMathematical Physics.
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
700 1 _aBlümlein, Johannes.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aSchneider, Carsten.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030802189
776 0 8 _iPrinted edition:
_z9783030802202
776 0 8 _iPrinted edition:
_z9783030802219
830 0 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x2197-8409
856 4 0 _uhttps://doi.org/10.1007/978-3-030-80219-6
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