Search results for "Tensor rank"
showing 3 items of 3 documents
One-loop integrals with XLOOPS-GiNaC
2001
We present a new algorithm for the reduction of one-loop tensor Feynman integrals within the framework of the XLOOPS project, covering both mathematical and programming aspects. The new algorithm supplies a clean way to reduce the one-loop one-, two- and three-point Feynman integrals with arbitrary tensor rank and powers of the propagators to a basis of simple integrals. We also present a new method of coding XLOOPS in C++ using the GiNaC library.
oneloop 2.0 — A program package calculating one-loop integrals
1997
We present an improved version of our program package oneloop which -- written as a package for MAPLE -- solves one-loop Feynman integrals. The package is calculating one-, two- and three-point functions both algebraically and numerically to any tensor rank. In addition to the original version oneloop 2.0 also calculates infrared divergent integrals. Higher powers of propagator terms and the $O(\eps)$ parts relevant for two-loop calculations are now supported.
The Rank of Trifocal Grassmann Tensors
2019
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerat…