New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of ...

it is well-known that “casual conditional” in islamic logics has been used with two meanings: “specific conditional” and “general conditional”. however, viewing the works of the muslim logicians, we find out that these two meanings of “casual conditional” have been interpreted in two various ways: each of the general and specific conditionals is sometimes interpreted as the condition of “non-ne...

The Differential equation method: calculation of vertex-type diagrams with one non-zero mass Abstract The differential equation method is applied to evaluate analytically two-loop vertex Feynman diagrams. Three on-shell infrared divergent planar two-loop diagrams with zero thresholds contributing to the processes Z → bb (for zero b mass) and/or H → gg are calculated in order to demonstrate a ne...

One and two loop self-energies are worked out explicitly for a heavy scalar field interacting weakly with a light self-interacting scalar field at finite temperature. The ring/daisy diagrams and a set of necklace diagrams can be summed simultaneously. This simple model serves to illustrate the connection between multi-loop self-energy diagrams and multiple scattering in a medium. PACS numbers: ...