On the Periods of Some Feynman Integrals
نویسنده
چکیده
We define some families of graphs and show that their graph hypersurfaces relative to coordinate simplices define mixed Tate motives. We show that the corresponding Feynman integrals evaluate to multiple zetas. Let G be a connected graph. To each edge e ∈ EG associate a variable αe, known as a Schwinger parameter, and consider the graph polynomial
منابع مشابه
Evaluating multiloop Feynman integrals by Mellin-Barnes representation
When calculating physical quantities that describe a given process one needs to evaluate a lot of Feynman integrals. After a tensor reduction based on some projectors (see, e.g., [1]) a given Feynman graph generates various scalar Feynman integrals that have the same structure of the integrand with various distributions of powers of propagators. A straightforward analytical strategy is to evalu...
متن کاملSome recent results on evaluating Feynman integrals
where ki, i = 1, . . . , h, are loop momenta and the denominators Er are either quadratic of linear with respect to ki and external momenta q1, . . . , qN . By default, the integrals are dimensionally regularized with d = 4− 2ǫ. If the number of Feynman integrals needed for a given calculation is small or/and they are simple, one evaluates, by some methods, every scalar Feynman integral of the ...
متن کاملConsiderations on Some Algebraic Properties of Feynman Integrals
Some algebraic properties of integrals over configuration spaces are investigated in order to better understand quantization and the Connes-Kreimer algebraic approach to renormalization. In order to isolate the mathematical-physics interface to quantum field theory independent from the specifics of the various implementations, the sigma model of Kontsevich is investigated in more detail. Due to...
متن کاملPeriods and Feynman integrals
We consider multi-loop integrals in dimensional regularisation and the corresponding Laurent series. We study the integral in the Euclidean region and where all ratios of invariants and masses have rational values. We prove that in this case all coefficients of the Laurent series are periods.
متن کاملApplying Gröbner Bases to Solve Reduction Problems for Feynman Integrals
We describe how Gröbner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Gröbner-type bases associated with polynomials of shift operators...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009