English

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

High Energy Physics - Theory 2014-11-18 v2

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.

Keywords

Cite

@article{arxiv.0801.2856,
  title  = {Quantum periods: A census of \phi^4-transcendentals},
  author = {Oliver Schnetz},
  journal= {arXiv preprint arXiv:0801.2856},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-21T10:04:13.309Z