✦ LIBER ✦

Where do the tedious products of ζ's come from?

✍ Scribed by D.J. Broadhurst

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 399 KB
Volume: 116
Category: Article
ISSN: 0920-5632
DOI: 10.1016/s0920-5632(03)80214-1

No coin nor oath required. For personal study only.

✦ Synopsis

Lamentably, the full analytical content of the s-expansion of the master two-loop two-point function, with arbitrary self-energy insertions in 4 -2e dimensions, is still unknown. Here we show that multiple zeta values (MZVs) of weights up to 12 suffice through o(eg). Products of primitive MZVs are generated by a processes of "pseudo-exponentiation" whose combinatorics faithfully accord with expectations based on Kreimer's modified shuffle product and on the Drinfeld-Deligne conjecture. The existence of such a mechanism, relating thousands of complicated rational numbers, enables us to identify precise and simple combinations of MZVs specific to quantum field theories in even numbers of spacetime dimensions.

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