Quantum periods: A census of φ^4-transcendentals

Details Quantum periods: A census of φ^4-transcendentals Quantum periods: A census of φ^4-transcendentals

2008-01-18

arxiv.org/abs/0801.2856v2

Communications in Number Theory and Physics, 4 no. 1 (2010), 1-48

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, 71 postscript figures, v2: augmented and rewritten

Scientific paper

Perturbative quantum field theories frequently feature rational linear combinations of multiple zeta values (periods). In massless \phi^4-theory we show that the periods originate from certain `primitive' vacuum graphs. Graphs with vertex connectivity 3 are reducible in the sense that they lead to products of periods with lower loop order. A new `twist' identity amongst periods is proved and a list of graphs (the census) with their periods, if available, is given up to loop order 8.

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