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A novel approach to integration by parts reduction. (English) Zbl 1330.81151
Summary: Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on Laporta’s algorithm. The key idea is to construct algebraic identities from numerical samples obtained from reductions over finite fields. We expect the method to be highly amenable to parallelization, show a low memory footprint during the reduction step, and allow for significantly better run-times.

81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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[1] Tkachov, F. V., Phys. Lett. B, 100, 65, (1981)
[2] Chetyrkin, K. G.; Tkachov, F. V., Nucl. Phys. B, 192, 159, (1981)
[3] Gorishnii, S. G.; Larin, S. A.; Surguladze, L. R.; Tkachov, F. V., Comput. Phys. Commun., 55, 381, (1989)
[4] Laporta, S., Int. J. Mod. Phys. A, 15, 5087, (2000)
[5] Anastasiou, C.; Lazopoulos, A., J. High Energy Phys., 0407, 046, (2004)
[6] Smirnov, A. V., J. High Energy Phys., 0810, 107, (2008)
[7] Smirnov, A. V.; Smirnov, V. A., Comput. Phys. Commun., 184, 2820, (2013)
[8] Studerus, C., Comput. Phys. Commun., 181, 1293, (2010)
[9] von Manteuffel, A.; Studerus, C.
[10] Lee, R. N.
[11] von zur Gathen, J.; Gerhard, J., Modern computer algebra, (2013), Cambridge University Press · Zbl 1277.68002
[12] Kant, P., Comput. Phys. Commun., 185, 1473, (2014)
[13] Wang, P. S., (Proceedings of SYMSAC ’81, (1981), ACM Press), 212
[14] Wang, P. S.; Guy, M. J.T.; Davenport, J. H., SIGSAM Bull., 16, 2, 2, (1982)
[15] Monagan, M., (Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, ISSAC ’04, (2004)), 243
[16] Khodadad, S.; Monagan, M., (Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ISSAC ’06, (2006)), 184
[17] Kauers, M., Nucl. Phys. B, Proc. Suppl., 183, 245, (2008), visit http://www.risc.jku.at/education/courses/ss2012/ca2/LinearSystemSolver.m to obtain an accompanying software package
[18] P. Kant, private communication.
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