# Sinc function representation and three-loop master diagrams

@article{Easther2001SincFR, title={Sinc function representation and three-loop master diagrams}, author={Richard Easther and Gerald S. Guralnik and Stephen C. Hahn}, journal={Physical Review D}, year={2001}, volume={63}, pages={085017} }

We test the Sinc function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc function representation converges rapidly, and it is straightforward to obtain accuracies of 1 part in 10{sup 6} for these diagrams and with longer runs we found results better than 1 part in…

## 2 Citations

Of Two Novel Numerical Methods in QFT

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- 2003

We outline two alternative schemes to perform numerical calculations in quantum field theory. In principle, both of these approaches are better suited to study phase structure than conventional Monte…

## References

SHOWING 1-10 OF 34 REFERENCES

An approach to the calculation of many-loop massless Feynman integrals

- Mathematics
- 1985

A generalization of the identity of dimensionless regular-zation is proposed. The generalization is used to divide the complete set of dimensionally (and analytically) regularized Feynman integrals…

Knots and Numbers in ϕ4 Theory to 7 Loops and Beyond

- Computer Science
- 1995

The investigations reported here entailed intensive use of REDUCE, to generate O(104) lines of code for multiple precision FORTRAN computations, enabled by Bailey’s MPFUN routines, running for O(103) CPUhours on DecAlpha machines.

Numerical Methods Based on Sinc and Analytic Functions

- Mathematics
- 1993

Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and…

Three-loop on-shell charge renormalization without integration:
$$\Lambda _{QED}^{\overline {MS} } $$
to four loops

- Physics
- 1992

AbstractUsing algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF32 series, whose…

MATH

- Biology
- 1992

It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.