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We comment on the algorithm to compute periods using hyperlogarithms, applied to massless Feynman integrals in the parametric representation.
doi:10.1016/0550-3213(81)90199-1
K. G. Chetyrkin, F. V. Tkachov, Integration by parts: The algorithm to calculate β \beta -functions in 4 loops, Nuclear Physics B 192 (1981) 159–204 · 1981
Earlier work this paper cites.
J. C. Collins, Renormalization, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 1984
1984
Earlier work this paper cites.
doi:10.1007/BF01018044
D. I. Kazakov, Calculation of Feynman Integrals by the Method of “Uniqueness”, Theor.Math.Phys. 58 (1984) 223–230 · 1984
Earlier work this paper cites.
doi:10.1007/BF01412581
D. T. Barfoot, D. J. Broadhurst, Z 2 × S 6 Z_{2}\times S_{6} symmetry of the two-loop diagram, Zeitschrift für Physik C Particles and Fields 41 (1) (1988) 81–85 · 1988
Earlier work this paper cites.
arXiv:hep-ph/9504352
D. J. Broadhurst, D. Kreimer, Knots and numbers in ϕ 4 \phi^{4} theory to 7 loops and beyond, Int.J.Mod.Phys. C6 (1995) 519–524 · 1995
Earlier work this paper cites.
arXiv:hep-ph/0308311
I. Bierenbaum, S. Weinzierl, The massless two-loop two-point function, European Physical Journal C 32 (2003) 67–78 · 2003
Earlier work this paper cites.
C. Itzykson, J.-B. Zuber, Quantum Field Theory, Dover publications, inc., 2005
2005
Earlier work this paper cites.
arXiv:hep-ph/0505174
S. Bekavac, Calculation of massless Feynman integrals using harmonic sums, Comput.Phys.Commun. 175 (2006) 180–195 · 2006
Cited alongside, same era.
F. C. S. Brown, The Massless Higher-Loop Two-Point Function, Communications in Mathematical Physics 287 (2009) 925–958 · 2009
Cited alongside, same era.
P. A. Baikov, K. G. Chetyrkin, Four loop massless propagators: An algebraic evaluation of all master integrals, Nuclear Physics B 837 (2010) 186–220 · 2010
Cited alongside, same era.
R. N. Lee, A. V. Smirnov, V. A. Smirnov, Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in ϵ \epsilon , Nuclear Physics B Proceedings Supplements 205–206 (2010) 308–313 · 2010
Cited alongside, same era.
R. N. Lee, A. V. Smirnov, V. A. Smirnov, Master integrals for four-loop massless propagators up to weight twelve, Nuclear Physics B 856 (2012) 95–110 · 2011
Later among the works it cites.
F. C. S. Brown, K. Yeats, Spanning Forest Polynomials and the Transcendental Weight of Feynman Graphs, Communications in Mathematical Physics 301 (2011) 357–382 · 2011
Later among the works it cites.
A. G. Grozin, Massless Two-Loop Self-Energy Diagram: Historical Review, International Journal of Modern Physics A 27 (2012) 30018 · 2012
Later among the works it cites.
E. Panzer, result data for 3- and 4-loop massless propagators (May 2013). URL http://www.mathematik.hu-berlin.de/~panzer/
2013
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A. V. Smirnov, M. Tentyukov, Four-loop massless propagators: A numerical evaluation of all master integrals, Nuclear Physics B 837 (2010) 40–49 · 2010
Cited alongside, same era.
O. Schnetz, Quantum periods: A Census of ϕ 4 \phi^{4} -transcendentals, Commun.Num.Theor.Phys. 4 (2010) 1–48 · 2010
Cited alongside, same era.
R. N. Lee, A. V. Smirnov, V. A. Smirnov, On epsilon expansions of four-loop non-planar massless propagator diagrams, European Physical Journal C 71 (2011) 1708 · 2011
Cited alongside, same era.
O. Schnetz, zeta_procedures . URL http://www.mathematik.hu-berlin.de/~kreimer/index.php?section=program&lang=en
Cited in the paper.
F. C. S. Brown, On the periods of some Feynman integrals, ArXiv e-prints arXiv:0910.0114
Cited in the paper.
F. C. S. Brown, O. Schnetz, Proof of the zig-zag conjecture, ArXiv e-prints arXiv:1208.1890
Cited in the paper.
Cited in the paper.
D. Kreimer, M. Sars, W. D. van Suijlekom, Quantization of gauge fields, graph polynomials and graph cohomology, Annals of PhysicsIn press
Cited in the paper.
F. C. S. Brown, D. Kreimer, Angles, scales and parametric renormalization, Letters in Mathematical Physics 103 (9) (2013) 933–1007 · 2013
Closest in time.
D. Kreimer, E. Panzer, Renormalization and Mellin transforms, in: C. Schneider, J. Blümlein (Eds.), Computer Algebra in Quantum Field Theory, Vol. XII of Texts & Monographs in Symbolic Computation, Springer Wien, 2013, pp. 195–223 · 2013
Closest in time.
D. Kreimer, Quantum fields, periods and algebraic geometry , in: PM2012 - Periods and Motives (Madrid, July 2–6, 2012), 2013, to appear. URL http://www.mathematik.hu-berlin.de/~maphy/MadridAMS.pdf
2013
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