Bibliographic notes:
[1] q-alg/9607022,
Kreimer, Renormalization and Knot Theory, to appear in J.Knot Th.Ram.,
final version of Habilitationsschrift; rational numbers from ladders and rainbows; two-braid torus knots give odd zetas.
[2] hep-th/9503059,
Kreimer, Knots and Divergences, PLB354, 117 (1995),
three braid knot 8_19 identified with David's first non-zeta discovery.
[3] hep-ph/9504352,
Broadhurst and Kreimer, Knots and Numbers in phi^4 Theory to 7 Loops and beyond, IJMP C6, 519 (1995),
strong confirmation of [1,2]; at 7 loops first irreducible triple sum identified with unique positive four-braid knot.
[4] hep-ph/9509296,
Broadhurst, Delbourgo and Kreimer, Unknotting the polarized vacuum of quenched QED, PLB366, 421 (1996),
cancellations of knots and transcendentals follows cancellations of subdivergences due to Ward identity; pattern extends to scalar QED.
[5] hep-th/9604128,
Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot and field theory, to appear in JMP,
a pair of 12-crossing 3-braids requires two transcendentals; one is an alternating sum unexpected in number theory; alternating sums enumerated.
[6] hep-th/9607174,
Broadhurst, Gracey and Kreimer, Beyond the triangle and uniqueness relations: Non-zeta counterterms at large N from positive knots, to appear in ZPhysC,
multiple zeta values and knots associated to all weights and crossings via epsilon-expansion of critical exponents.
[7] hep-th/9609128,
Broadhurst and Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, to appear in PLB,
non-MZV transcendentals appear at 10 crossings; subset of positive knots identified with MZVs to 15 crossings; conjectured enumeration of irreducible MZVs graded by depth and weight.
[8] hep-th/9610128,
Kreimer, On Knots in subdivergent Diagrams, subm. to NPB,
2-braid torus knots, and hence odd zetas, from dressing ladders and rainbows; zeta(4) and higher powers of pi^2 from framing dependence.
[9] hep-th/9611004,
Borwein, Bradley and Broadhurst, Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k, to appear in El.J.Comb.,
many results for MZVs and alternating sums inferred from huge database acquired in [5]; some proved; most still conjectured.
[10] hep-th/9612010,
Kreimer, Weight systems from Feynman Diagrams,
four-term relation derived for subdivergence-free counterterms; sufficient conditions established; some hints of an STU-relation underlying this.
[11] hep-th/9612011,
Broadhurst and Kreimer, Feynman Diagrams as a weight system: Four-loop test of a four-term relation,
confirmation of firm prediction of [10] at 4 loops, and of STU-type relation at 5 loops; suggestion of further structure at 5 loops.
[12] hep-th/9612012,
Broadhurst, Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams,
BK conjectured enumeration in [7] spectacularly confirmed at depths 4 and 5; motivation for Ansatz given by push-down discovered in [5,6].
[13] hep-th/9612013,
Broadhurst and Kotikov, Compact analytical form for non- zeta terms in critical exponents at order 1/N^3,
BGK epsilon-expansions of [6] confirmed for sigma model and phi^4 theory; at D=3 alternating irreducibles emerge as in massive 4-D calculations.
[14] in preparation, Borwein, Bradley, Broadhurst and Girgensohn, CECM report,
development of proofs for [9] and further testing of [5,7,12].
[15] in preparation, Kreimer, Knots and Feynman Diagrams, to be published by Cambridge University Press,
manuscript completion by March 1997, all the above and more.
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