Built on

D. J. Broadhurst, “Summation of an infinite series of ladder diagrams,” Phys. Lett. B 307
1993
Earlier work this paper cites.
A. B. Goncharov “Polylogarithms and Motivic Galois groups,” Proc. Symp. Pure Math. 55
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, “Dimensionally regulated pentagon integrals,” Nucl. Phys. B 412
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, “One loop selfdual and N = 4 N=4 superYang-Mills,” Phys. Lett. B 394
1997
Earlier work this paper cites.
A. B. Goncharov, “Multiple polylogarithms, cyclotomy and modular complexes,” Math. Res. Lett. 5
1998
Earlier work this paper cites.
A. Goncharov, “Volumes of hyperbolic manifolds and mixed Tate motives,” J. AMS 12
1999
Earlier work this paper cites.
A. B. Goncharov, “Galois symmetries of fundamental groupoids and noncommutative geometry,” Duke Math J. 128
2005
Earlier work this paper cites.
V. Smirnov, Feynman Integral Calculus
2006
Earlier work this paper cites.

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2011

Symbols of One-Loop Integrals From Mixed Tate Motives

Spradlin, Marcus, Volovich, Anastasia

Understand

We use a result on mixed Tate motives due to Goncharov (arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop 2m-gon integral in 2m dimensions may be read off directly from its Feynman parameterization.

The algorithm proceeds via recursion in m seeded by the well-known box integrals in four dimensions.
As a simple application of this method we write down the symbol of a three-mass hexagon integral in six dimensions.

Built on

D. J. Broadhurst, “Summation of an infinite series of ladder diagrams,” Phys. Lett. B 307
1993
Earlier work this paper cites.
A. B. Goncharov “Polylogarithms and Motivic Galois groups,” Proc. Symp. Pure Math. 55
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon and D. A. Kosower, “Dimensionally regulated pentagon integrals,” Nucl. Phys. B 412
1994
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, “One loop selfdual and N = 4 N=4 superYang-Mills,” Phys. Lett. B 394
1997
Earlier work this paper cites.
A. B. Goncharov, “Multiple polylogarithms, cyclotomy and modular complexes,” Math. Res. Lett. 5
1998
Earlier work this paper cites.
A. Goncharov, “Volumes of hyperbolic manifolds and mixed Tate motives,” J. AMS 12
1999
Earlier work this paper cites.
A. B. Goncharov, “Galois symmetries of fundamental groupoids and noncommutative geometry,” Duke Math J. 128
2005
Earlier work this paper cites.
V. Smirnov, Feynman Integral Calculus
2006
Earlier work this paper cites.