000 03900nam a22005775i 4500
001 978-3-7091-1616-6
003 DE-He213
005 20200420221254.0
007 cr nn 008mamaa
008 131005s2013 au | s |||| 0|eng d
020 _a9783709116166
_9978-3-7091-1616-6
024 7 _a10.1007/978-3-7091-1616-6
_2doi
050 4 _aQC793-793.5
050 4 _aQC174.45-174.52
072 7 _aPHQ
_2bicssc
072 7 _aSCI051000
_2bisacsh
082 0 4 _a539.72
_223
245 1 0 _aComputer Algebra in Quantum Field Theory
_h[electronic resource] :
_bIntegration, Summation and Special Functions /
_cedited by Carsten Schneider, Johannes Bl�umlein.
264 1 _aVienna :
_bSpringer Vienna :
_bImprint: Springer,
_c2013.
300 _aXIV, 411 p. 41 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x0943-853X
505 0 _aHarmonic sums, polylogarithms, special numbers, and their generalizations -- Multiple Zeta values and modular forms in quantum field theory -- Computer-assisted proofs of some identities for Bessel functions of fractional order -- Conformal methods for massless Feynman integrals and large Nf methods -- The holonomic toolkit -- Orthogonal polynomials -- Creative telescoping for holonomic functions -- Renormalization and Mellin transforms -- Relativistic Coulomb integrals and Zeilberger's holonomic systems approach -- Hypergeometric functions in Mathematica -- Solving linear recurrence equations with polynomial coefficients -- Generalization of Risch's algorithms to special functions -- Multiple hypergeometric series -- Appell series and beyond -- Simplifying multiple sums in difference fields -- Potential of FORM 4.0 -- Feynman graphs.
520 _aThe book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.
650 0 _aPhysics.
650 0 _aComputer science
_xMathematics.
650 0 _aSpecial functions.
650 0 _aMathematical physics.
650 0 _aQuantum field theory.
650 0 _aString theory.
650 0 _aElementary particles (Physics).
650 1 4 _aPhysics.
650 2 4 _aElementary Particles, Quantum Field Theory.
650 2 4 _aMathematical Physics.
650 2 4 _aQuantum Field Theories, String Theory.
650 2 4 _aSpecial Functions.
650 2 4 _aSymbolic and Algebraic Manipulation.
700 1 _aSchneider, Carsten.
_eeditor.
700 1 _aBl�umlein, Johannes.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783709116159
830 0 _aTexts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria,
_x0943-853X
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7091-1616-6
912 _aZDB-2-SCS
942 _cEBK
999 _c52794
_d52794