Iterated Integrals Related to Feynman Integrals Associated to Elliptic Curves
نویسندگان
چکیده
This talk reviews Feynman integrals, which are associated to elliptic curves. The will give an introduction into the mathematics behind them, covering topics of curves, modular forms and moduli space $n$ marked points on a genus one curve. latter be important, as integrals can expressed iterated ${\mathcal M}_{1,n}$, in same way evaluate multiple polylogarithms M}_{0,n}$. With right language, many methods from zero case carry over case. In particular we see specific examples that differential equation for cast $\varepsilon$-form. allows systematically obtain solution order by dimensional regularisation parameter.
منابع مشابه
Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as 2F1 Gauß hypergeomet...
متن کاملIterated integrals, diagonal cycles and rational points on elliptic curves
The theme of this article is the connection between the pro-unipotent fundamental group π1(X; o) of a pointed algebraic curve X, algebraic cycles, and special values of Lfunctions. The extension of mixed Hodge structures arising in the second stage in the lower central series of π1(X; o) gives rise to a supply of complex points on the Jacobian Jac(X) of X, indexed by Hodge cycles on X ×X. The m...
متن کاملMaPhy-AvH/2014-10 FEYNMAN INTEGRALS AND ITERATED INTEGRALS ON MODULI SPACES OF CURVES OF GENUS ZERO
This paper describes algorithms for the exact symbolic computation of period integrals on moduli spaces M0,n of curves of genus 0 with n ordered marked points, and applications to the computation of Feynman integrals.
متن کاملDouble Integrals and Iterated Integrals
Corresponding material in the book: Section 15.2, 15.3. Note: We are omitting the question types from the book that require three-dimensional visualization, i.e., those that require sketching figures in three dimensions to compute volumes. What students should definitely get: The procedure for computing double integrals over rectangles using iterated integrals, the procedure for computing doubl...
متن کاملSome methods to evaluate complicated Feynman integrals
Last years there was an essential progress in calculations of Feynman integrals. It seems that most important results have been obtained for two-loop four-point massless Feynman diagrams: in on-shall case (see [1,2]) and for a class of offshall legs (see [3]). A review of the results can be found in [4]. Moreover, very recently results for a class of these diagrams have been obtained [5] in the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Texts and monographs in symbolic computation
سال: 2021
ISSN: ['0943-853X', '2197-8409']
DOI: https://doi.org/10.1007/978-3-030-80219-6_20