Integral reduction with Kira 2.0 and finite field methods. (English) Zbl 1523.81078
Summary: We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. This procedure can be parallelized on computer clusters with MPI. Furthermore, the support for user-provided systems of equations has been significantly improved. This mode provides the flexibility to integrate Kira into projects that employ specialized reduction formulas, direct reduction of amplitudes, or to problems involving linear system of equations not limited to relations among standard Feynman integrals. We show examples from state-of-the-art Feynman integral reduction problems and provide benchmarks of the new features, demonstrating significantly reduced main memory usage and improved performance w.r.t. previous versions of Kira.
MSC:
| 81Q30 | Feynman integrals and graphs; applications of algebraic topology and algebraic geometry |
| 81S40 | Path integrals in quantum mechanics |
| 81T33 | Dimensional compactification in quantum field theory |
| 03H15 | Nonstandard models of arithmetic |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
Feynman diagrams; multi-loop Feynman integrals; dimensional regularization; Laporta algorithm; modular arithmetic; computer algebraReferences:
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