Quantum periods: A census of\phi^ 4-transcendentals
O Schnetz - arXiv preprint arXiv:0801.2856, 2008 - arxiv.org
arXiv preprint arXiv:0801.2856, 2008•arxiv.org
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 certainprimitive'vacuum graphs. Graphs with vertex connectivity 3 are reducible in the
sense that they lead to products of periods with lower loop order. A newtwist'identity
amongst periods is proved and a list of graphs (the census) with their periods, if available, is
given up to loop order 8.
multiple zeta values (periods). In massless\phi^ 4-theory we show that the periods originate
from certainprimitive'vacuum graphs. Graphs with vertex connectivity 3 are reducible in the
sense that they lead to products of periods with lower loop order. A newtwist'identity
amongst periods is proved and a list of graphs (the census) with their periods, if available, is
given up to loop order 8.
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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