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arXiv · 0801.2856

Quantum periods: A census of \phi^4-transcendentals

Oliver Schnetz
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Abstract

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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Oliver Schnetz. 2008-01-18. Quantum periods: A census of \phi^4-transcendentals. https://arxiv.org/abs/0801.2856

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