Reduction of Feynman integrals in the parametric representation

Feynman path integrals on phase space and the metaplectic representation

heterogeneity within the orientalist discourse: representation of the orient in womens travelogues and mens paintings

from 1950s onward, new theories and critical approaches burgeoned across humanities. these theories were context-oriented; as a result, the analysis of discursive practices gained significance. thus, social, political, historical and cultural discourses that have been hitherto marginalized and considered inferior to literary texts, were introduced as important texts to be analyzed by critics. o...

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...

Applying 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...

Transformation, Reduction and Extrapolation Techniques for Feynman Loop Integrals

We address the computation of Feynman loop integrals, which are required for perturbation calculations in high energy physics, as they contribute corrections to the scattering amplitude for the collision of elementary particles. Results in this field can be used in the verification of theoretical models, compared with data measured at colliders. We made a numerical computation feasible for vari...