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arxiv: 0801.2856 · v2 · pith:VBBIHPVUnew · submitted 2008-01-18 · ✦ hep-th

Quantum periods: A census of φ⁴-transcendentals

classification ✦ hep-th
keywords periodsgraphscensuslooporderquantumamongstavailable
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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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