Related papers: Massless and massive one-loop three-point function…
It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…
We (re)derive the propagators and Feynman rules for the massless scalar and vector multiplets in N=2 Projective Superspace ('Projective Hyperspace'). With these, we are able to calculate both the divergent and finite parts of 2, 3 & 4-point…
Using the method of uniqueness a two-loop massless propagator Feynman diagram with a non-integer index on the central line is evaluated in a very transparent way. The result is applied to the computation of the two-loop polarization…
A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.
A direct link between a one-loop N-point Feynman diagram and a geometrical representation based on the N-dimensional simplex is established by relating the Feynman parametric representations to the integrals over contents of…
We present a generally applicable reduction formalism which makes it possible to express an arbitrary tensor and scalar one-loop Feynman integral, with N external lines and massless propagators, in terms of a basic set of eight fundamental…
A recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V.…
A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…
A set of one-loop vertex and box tensor-integrals with massless internal particles has been obtained directly without any reduction method to scalar-integrals. The results with one or two massive external lines for the vertex integral and…
We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
``Three-mass triangles'' are a class of integral functions appearing in one-loop gauge theory amplitudes. We discuss how the complex analytic properties and singularity structures of these amplitudes can be combined with generalised…
Recently, infinite families of massive Feynman integrals were found to feature an unexpected Yangian symmetry. In the massless case, similar integrability properties are understood via the interpretation of individual Feynman integrals as…
We present a system of canonical differential equations satisfied by the three-loop banana integrals with four distinct non-zero masses in $D = 2-2\eps$ dimensions. Together with the initial condition in the small-mass limit, this provides…
In this work, we mainly study the one-loop effective action for real scalar theories in non-homogeneous backgrounds in odd dimensions. It is shown that through the method studied in Ref. [1], it is possible to obtain a unified result for…
This paper explores the idea that within the framework of three-dimensional quantum gravity one can extend the notion of Feynman diagram to include the coupling of the particles in the diagram with quantum gravity. The paper concentrates on…
We develop a systematic projector-based Feynman diagram framework that intrinsically encodes quantum geometry for nonlinear optical responses. By explicitly incorporating geometric quantities such as the quantum geometric tensor, quantum…
Extending the method successful for one-loop integrals, the computation of two-loop diagrams with general internal masses is discussed. For the two-loop vertex of non-planar type, as an example, we show a calculation related to…
N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop…
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…