Fetching the paper…
Reading the bibliography…
During the last several years remarkable progress has been made in numerical calculations of dimensionally regulated multi-loop Feynman diagrams using Mellin-Barnes (MB) representations.
doi:10.1112/plms/s2-6.1.141
E. W. Barnes, A new development of the theory of the hypergeometric functions, Proc. Lond. Math. Soc. (2) 6 (1908) 141–177 · 1908
Earlier work this paper cites.
doi:10.1103/PhysRev.75.486
F. J. Dyson, The Radiation theories of Tomonaga, Schwinger, and Feynman, Phys. Rev. 75 (1949) 486–502 · 1949
Earlier work this paper cites.
doi:10.1103/PhysRev.75.1736
F. J. Dyson, The S matrix in quantum electrodynamics, Phys. Rev. 75 (1949) 1736–1755 · 1949
Earlier work this paper cites.
doi:10.1103/PhysRev.76.749
R. P. Feynman, The Theory of positrons, Phys. Rev. 76 (1949) 749–759 · 1949
Earlier work this paper cites.
doi:10.1103/PhysRev.76.769
R. P. Feynman, Space-time approach to quantum electrodynamics, Phys. Rev. 76 (1949) 769–789 · 1949
Earlier work this paper cites.
E. Whittaker, G. Watson, A course of modern analysis, Cambridge University Press, 1965
1965
Earlier work this paper cites.
doi:10.1007/BF01609168
M. C. Bergere, Y.-M. P. Lam, Asymptotic expansion of Feynman amplitudes. Part 1: The convergent case, Commun. Math. Phys. 39 (1974) 1 · 1974
Earlier work this paper cites.
N.I. Ussyukina, On a Representation for Three Point Function, Teor.Mat.Fiz. 22, 300 (1975)
1975
Earlier work this paper cites.
F. Pham, Vanishing homologies and the n n variable saddlepoint method, Singularities, Summer Inst., Arcata/Calif. 1981, Proc. Symp. Pure Math. 40, Part 2, 319-333 (1983) (1983)
1983
Earlier work this paper cites.
doi:10.1016/0370-2693(91)90413-K
A. Kotikov, Differential equations method: New technique for massive Feynman diagrams calculation, Phys. Lett. B254 (1991) 158–164 · 1991
Earlier work this paper cites.
A. Kotikov, Differential equations method: The Calculation of vertex type Feynman diagrams, Phys. Lett. B259 (1991) 314–322
1991
Earlier work this paper cites.
A. V. Kotikov, Differential equation method: The Calculation of N point Feynman diagrams, Phys. Lett. B267 (1991) 123–127
1991
Earlier work this paper cites.
doi:10.1016/0010-4655(91)90002-3
G. van Oldenborgh, FF: A Package to evaluate one loop Feynman diagrams, Comput. Phys. Commun. 66 (1991) 1–15 · 1991
Earlier work this paper cites.
S. S. Schweber, QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga, Princeton, USA, Univ. Pr. (1994) 732 p
1994
Earlier work this paper cites.
arXiv:hep-th/9711188
E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A110 (1997) 1435–1452 · 1997
Earlier work this paper cites.
arXiv:hep-ph/9905323
V. A. Smirnov, Analytical result for dimensionally regularized massless on shell double box, Phys. Lett. B460 (1999) 397–404 · 1999
Earlier work this paper cites.
arXiv:hep-ph/9909506
J. Tausk, Nonplanar massless two loop Feynman diagrams with four on-shell legs, Phys. Lett. B469 (1999) 225–234 · 1999
Earlier work this paper cites.
C. Bender, S. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory , Advanced Mathematical Methods for Scientists and Engineers, Springer, 1999. URL https://books.google.pl/books?id=-yQXwhE6iWMC
1999
Earlier work this paper cites.
arXiv:hep-ph/0012260
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418–431 · 2001
Earlier work this paper cites.
R. Wong, Asymptotic Approximation of Integrals , Classics in Applied Mathematics, Society for Industrial and Applied Mathematics, 2001. URL https://books.google.pl/books?id=KQHPHPZs8k4C
2001
Earlier work this paper cites.
V. Smirnov, “Applied Asymptotic Expansions in Momenta and Masses” (Springer Verlag, Berlin, 2002)
2002
Earlier work this paper cites.
arXiv:hep-ph/0201075
M. Steinhauser, Results and techniques of multiloop calculations, Phys. Rept. 364 (2002) 247–357 · 2002
Earlier work this paper cites.
V. Smirnov, “Evaluating Feynman Integrals” (Springer Verlag, Berlin, 2004)
2004
Cited alongside, same era.
V. Smirnov, Evaluating Feynman integrals, Springer Tracts Mod. Phys. 211 (2004) 1–244
2004
Cited alongside, same era.
D. Kaiser, Drawing theories apart: the dispersion of Feynman diagrams in postwar physics , Chicago Univ. Press, Chicago, IL, 2005. URL http://cds.cern.ch/record/941915
2005
Cited alongside, same era.
arXiv:hep-ph/0404043
T. Hahn, CUBA: A library for multidimensional numerical integration, Comput. Phys. Commun. 168 (2005) 78–95 · 2005
Cited alongside, same era.
arXiv:hep-ph/0501132
S. P. Martin, D. G. Robertson, TSIL: A Program for the calculation of two-loop self-energy integrals, Comput. Phys. Commun. 174 (2006) 133–151 · 2005
Cited alongside, same era.
arXiv:hep-ph/0511200
M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559–571 · 2006
L. Nicolaescu, An Invitation to Morse Theory , Universitext, Springer New York, 2011. URL https://books.google.pl/books?id=nCgvt2MY4QAC
2011
Later among the works it cites.
E. Witten, Analytic Continuation Of Chern-Simons Theory, AMS/IP Stud. Adv. Math. 50 (2011) 347–446 · 2011
Later among the works it cites.
D. Harlow, J. Maltz, E. Witten, Analytic Continuation of Liouville Theory, JHEP 12 (2011) 071 · 2011
Later among the works it cites.
J. Fleischer, T. Riemann, V. Yundin, New developments in PJFry, PoS LL2012 (2012) 020, http://pos.sissa.it/…151/020/LL2012_020.pdf · 2012
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
arXiv:hep-ph/0511176
C. Anastasiou, A. Daleo, Numerical evaluation of loop integrals, JHEP 0610 (2006) 031 · 2006
Cited alongside, same era.
J. Gluza, K. Kajda, T. Riemann, AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals, Comput. Phys. Commun. 177 (2007) 879–893 · 2007
Cited alongside, same era.
arXiv:hep-ph/0703282
C. Anastasiou, S. Beerli, A. Daleo, Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically, JHEP 0705 (2007) 071 · 2007
Cited alongside, same era.
G. Ossola, C. G. Papadopoulos, R. Pittau, CutTools: A Program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 · 2008
Cited alongside, same era.
C. F. Berger, Z. Bern, L. J. Dixon, F. Febres Cordero, D. Forde, H. Ita, D. A. Kosower, D. Maitre, An Automated Implementation of On-Shell Methods for One-Loop Amplitudes, Phys. Rev. D78 (2008) 036003 · 2008
Cited alongside, same era.
R. K. Ellis, G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 · 2008
Cited alongside, same era.
A. Freitas, Numerical evaluation of multi-loop integrals using subtraction terms, JHEP 1207 (2012) 132 · 2012
Later among the works it cites.
A. Freitas, Y.-C. Huang, Electroweak two-loop corrections to s i n 2 θ eff b b ¯ sin^{2}{\theta}_{\rm eff}^{b{\bar{b}}} and R b R_{b} using numerical Mellin-Barnes integrals, JHEP 1208 (2012) 050 · 2012
Later among the works it cites.
V. Arnold, A. Varchenko, S. Gusein-Zade, Singularities of Differentiable Maps: Volume II Monodromy and Asymptotic Integrals , Monographs in Mathematics, Birkhäuser Boston, 2012. URL https://books.google.pl/books?id=1BAGCAAAQBAJ
2012
Later among the works it cites.
J. M. Henn, Multiloop integrals in dimensional regularization made simple, Phys. Rev. Lett. 110 (25) (2013) 251601 · 2013
Later among the works it cites.
C. Anastasiou, C. Duhr, F. Dulat, B. Mistlberger, Soft triple-real radiation for Higgs production at N3LO, JHEP 07 (2013) 003 · 2013
Later among the works it cites.
K. Bielas, I. Dubovyk, J. Gluza, T. Riemann, Some Remarks on Non-planar Feynman Diagrams, Acta Phys. Polon. B44 (2013) 2249–2255 · 2013
Later among the works it cites.
A. V. Smirnov, FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions, Comput. Phys. Commun. 185 (2014) 2090–2100 · 2014
Later among the works it cites.
B. Chokoufe Nejad, T. Hahn, J. N. Lang, E. Mirabella, FormCalc 8: Better Algebra and Vectorization, J. Phys. Conf. Ser. 523 (2014) 012050 · 2014
Later among the works it cites.
Y. Tanizaki, T. Koike, Real-time Feynman path integral with Picard-Lefschetz theory and its applications to quantum tunneling, Annals Phys. 351 (2014) 250–274 · 2014
Later among the works it cites.
S. Borowka, G. Heinrich, S. P. Jones, M. Kerner, J. Schlenk, T. Zirke, SecDec 3.0: numerical evaluation of multi-scale integrals beyond one loop, Comput. Phys. Commun. 196 (2015) 470–491 · 2015
Later among the works it cites.
T. Kanazawa, Y. Tanizaki, Structure of Lefschetz thimbles in simple fermionic systems, JHEP 03 (2015) 044 · 2015
Later among the works it cites.
I. Dubovyk, J. Gluza, T. Riemann, J. Usovitsch, Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions, PoS LL2016 (2016) 034 · 2016
Later among the works it cites.
I. Dubovyk, A. Freitas, J. Gluza, T. Riemann, J. Usovitsch, 30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop corrections to the Z b ¯ \bar{b} b vertex, PoS LL2016 (2016) 075 · 2016
Later among the works it cites.
I. Dubovyk, A. Freitas, J. Gluza, T. Riemann, J. Usovitsch, The two-loop electroweak bosonic corrections to sin 2 θ eff b \sin^{2}\theta_{\rm eff}^{\rm b} , Phys. Lett. B762 (2016) 184–189 · 2016
Later among the works it cites.
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider, Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra, Comput. Phys. Commun. 202 (2016) 33–112 · 2016
Later among the works it cites.
A. Freitas, Numerical multi-loop integrals and applications, Prog. Part. Nucl. Phys. 90 (2016) 201–240 · 2016
Later among the works it cites.
I. Dubovyk, J. Gluza, T. Riemann, J. Usovitsch, Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions, PoS LL2016 (2016) 034 · 2016
Later among the works it cites.
G. Cullen, N. Greiner, G. Heinrich, G. Luisoni, P. Mastrolia, G. Ossola, T. Reiter, F. Tramontano, Automated One-Loop Calculations with GoSam, Eur. Phys. J. C72 (2012) 1889 · 2034
Closest in time.