Quantum periods: A census of φ4-transcendentals

Communications in Number Theory and Physics

Volumn 4, Issue 1, 2010, Pages 1-47

  Schnetz, Oliver ^a  

^a Department Mathematik ^*  (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84864316837     PISSN: 19314523     EISSN: 19314531     Source Type: Journal    
DOI: 10.4310/CNTP.2010.v4.n1.a1     Document Type: Article

References (46)

1. T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Revised value of the eighth-order electron g - 2, Phys. Rev. Lett. 99 (2007), 110406.
2. T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Revised value of the eighth-order QED contribution to the anomalous magnetic moment of the electron, Phys. Rev. D77 (2008), 053012.
3. C.F. Berger, Z. Bern, L.J. Dixon, D. Forde and D.A. Kosower, On-shell unitarity bootstrap for QCD amplitudes, Nucl. Phys. Proc. Suppl. 160 (2006), 261-270.
4. S. Bloch, Motives associated to graphs, Japan. J. Math. 2 (2007), 165-196.
5. S. Bloch, H. Esnault and D. Kreimer, On motives associated to graph polynomials, Comm. Math. Phys. 267 (2006), 181-225.
6. J. Blümlein, D.J. Broadhurst and J.A.M. Vermaseren, The multiple zeta value data mine, (2009),
7. C. Bogner and S. Weinzierl, Periods and Feynman integrals, (2007)
8. R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005), 181602.
9. D.J. Broadhurst, Exploiting the 1,440-fold symmetry of the master twoloop diagram, Z. Phys. C32 (1986), 249-253.
10. 4 theory to 7 loops and beyond, Int. J. Mod. Phys. C6 (1995), 519-524.
11. D.J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory, (1996), arXiv:hep-th/9604128.
12. D.J. Broadhurst and D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B 393 (1997), 403-412.
13. F.C.S. Brown, The massless higher-loop two-point function, Comm. Math. Phys. 287(3) (2009), 925-958.
14. F.C.S. Brown, On the periods of some Feynman integrals, (2009),
15. F.C.S. Brown and K. Yeats, Spanning forest polynomials and the transcendental weight of feynman graphs, 2009, arXiv:0910.5429 [math-ph], accepted by Comm. Math. Phys.
16. K.G. Chetyrkin, A.L. Kataev and F.V. Tkachov, New approach to evaluation of multiloop Feynman integrals: The Gegenbauer polynomial x-space technique, Nucl. Phys. B 174 (1980), 345-377.
17. K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981), 159-204
18. A. Connes and D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem, Comm. Math. Phys. 210(1) (2000), 249-273.
19. A. Connes and D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem II: The β-function, diffeomorphisms and the renormalization group, Comm. Math. Phys. 216(1) (2001), 215-241.
20. A. Connes and M. Marcolli, Noncommutative geometry, quantum fields and motives, American Mathematical Society, Providence, RI, 2008.
21. D. Doryn, Cohomology of graph hypersurfaces associated to certain Feynman graphs, (2009),
22. K. Ebrahimi-Fard and D. Kreimer, Hopf algebra approach to Feynman diagram calculations, J. Phys. A 38 (2005), R385.
23. G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio and B. Odom, New determination of the fine structure constant from the electron g value and QED, Phys. Rev. Lett. 97 (2006) 030802; Phys. Rev. Lett. 99 (2007), 039902(E).
24. H. Gangl, M. Kaneko and D. Zagier, Double zeta values and modular forms, in 'Automorphic Forms and Zeta Functions', Proceedings of the Conference in Memory of Tsuneo Arakawa, World Scientific, Singapore, 2006.
25. A.B. Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry, (2004), arXiv:math/0208144v4.
26. D. Hanneke, S. Fogwell and G. Gabrielse, New measurement of the electron magnetic moment and the fine structure constant, Phys. Rev. Lett. 100 (2008), 120801.
27. J.C. Itzykson and J.B. Zuber, Quantum field theory, Mc-Graw-Hill, New York, 1980.
28. D.I. Kazakov, The method of uniqueness, a new powerful technique for multiloop calculations, Phys. Lett. B 133(6) (1983), 406.
29. M. Kontsevich and D. Zagier, Periods, in 'Mathematics Unlimited - 2001 and Beyond', eds. B. Engquis and W. Schmid, Springer-Verlag, Berlin, Heidelberg, New York, 2001, 771.
30. D. Kreimer, Knots and Feynman diagrams, Cambridge University Press, Cambridge, 2000.
31. 3 in QED, Phys. Lett. B 379 (1996), 283.
32. B.E. Lautrup, A. Peterman and E. de Rafael, Recent developments in the comparison between theory and experiments in Quantum electrodynamics, Phys. Rep. 3(4) (1972), 193-260.
33. L. Lovász, Combinatorial problems and exercises, North-Holland, Amsterdam, 1979.
34. B.D. McKay, nauty, 2007, http://cs.anu.edu.au/~bdm/nautyversion2.4ss7.
35. B. Odom, D. Hanneke, B. D'Urso and G. Gabrielse, New measurement of the electron magnetic moment using a one-electron quantum cyclotron, Phys. Rev. Lett. 97 (2006), 030801.
36. M. Passera, Electron, muon and tau magnetic moments: a theoretical update, Nucl. Phys. Proc. Suppl. 169 (2007), 213-225.
37. A. Peterman, Fourth order magnetic moment of the electron, Helv. Phys. Acta 30 (1957), 407-408 and Nucl. Phys. 5 (1958), 677-683.
38. E. de Rafael and J.L. Rosner, Short-distance behavior of quantum electrodynamics and the Callan-Symanzik equation for the photon propagator, Ann. Phys. 82 (1974), 369-406.
39. O. Schnetz, Calculation of the φ4 6-loop non-zeta transcendental, (1999), arXiv:hep-th/9912149.
40. O. Schnetz, Quantum periods: a census of φ4-transcendentals (version1), (2008), arXiv:0801.2856v1 [hep-th].
41. O. Schnetz, Quantum field theory over Fq, arXiv:0909.0905 [math.CO] (2009), submitted to Elec. J. Comb.
42. J. Schwinger, On quantum-electrodynamics and the magnetic moment of the electron, Phys. Rev. 73 (1947), 416-417.
43. C.M. Sommerfield, The magnetic moment of the electron, Phys. Rev. 107 (1957), 328-329 and Ann. Phys. 5 (1958), 26-57.
44. N.I. Ussyukina, Calculation of multiloop diagrams in high orders of perturbation theory, Phys. Lett. B 267 (1991), 382.
45. E. Witten, Perturbative gauge theory as a string theory in twistor space, Comm. Math. Phys. 252 (2004), 189-258.
46. D. Zagier, Values of zeta functions and their applications, First European Congress of Mathematics, Vol. II, 1992, 497, Birkhauser Boston, Cambridge MA, 1994