2,617 research outputs found
On the Invariance of Residues of Feynman Graphs
We use simple iterated one-loop graphs in massless Yukawa theory and QED to
pose the following question: what are the symmetries of the residues of a graph
under a permutation of places to insert subdivergences. The investigation
confirms partial invariance of the residue under such permutations: the highest
weight transcendental is invariant under such a permutation. For QED this
result is gauge invariant, ie the permutation invariance holds for any gauge.
Computations are done making use of the Hopf algebra structure of graphs and
employing GiNaC to automate the calculations.Comment: 24 pages, latex generated figures. Minor changes in revised versio
A Short Note on Two-Loop Box Functions
It is shown that the two-loop four-point functions are similar in structure
to the three-point two-loop functions for all mass cases and topologies. The
result is derived by using a rotation to a (+,-,-,+) signature without spoiling
analyticity properties.Comment: 7 pages, UTAS-PHYS-94-23, plain LATE
Unique factorization in perturbative QFT
We discuss factorization of the Dyson--Schwinger equations using the Lie- and
Hopf algebra of graphs. The structure of those equations allows to introduce a
commutative associative product on 1PI graphs. In scalar field theories, this
product vanishes if and only if one of the factors vanishes. Gauge theories are
more subtle: integrality relates to gauge symmetries.Comment: 5pages, Talk given at "RadCor 2002 - Loops and Legs 2002", Kloster
Banz, Germany, Sep 8-13, 200
The Structure of the Ladder Insertion-Elimination Lie algebra
We continue our investigation into the insertion-elimination Lie algebra of
Feynman graphs in the ladder case, emphasizing the structure of this Lie
algebra relevant for future applications in the study of Dyson-Schwinger
equations. We work out the relation of this Lie algebra to some classical
infinite dimensional Lie algebra and we determine its cohomology.Comment: 24 pages, LaTex, typos correcte
New mathematical structures in renormalizable quantum field theories
Computations in renormalizable perturbative quantum field theories reveal
mathematical structures which go way beyond the formal structure which is
usually taken as underlying quantum field theory. We review these new
structures and the role they can play in future developments.Comment: 26p,4figs., Invited Contribution to Annals of Physics, minor typos
correcte
Leading RG logs in theory
We find the leading RG logs in theory for any Feynman diagram with 4
external edges. We obtain the result in two ways. The first way is to calculate
the relevant terms in Feynman integrals. The second way is to use the RG
invariance based on the Lie algebra of graphs introduced by Connes and Kreimer.
The non-RG logs, such as , are discussed.Comment: 24 pages LaTeX, 12 figure
A new Method for Computing One-Loop Integrals
We present a new program package for calculating one-loop Feynman integrals,
based on a new method avoiding Feynman parametrization and the contraction due
to Passarino and Veltman. The package is calculating one-, two- and three-point
functions both algebraically and numerically to all tensor cases. This program
is written as a package for Maple. An additional Mathematica version is planned
later.Comment: 12 pages Late
What is the trouble with Dyson--Schwinger equations?
We discuss similarities and differences between Green Functions in Quantum
Field Theory and polylogarithms. Both can be obtained as solutions of fixpoint
equations which originate from an underlying Hopf algebra structure. Typically,
the equation is linear for the polylog, and non-linear for Green Functions. We
argue though that the crucial difference lies not in the non-linearity of the
latter, but in the appearance of non-trivial representation theory related to
transcendental extensions of the number field which governs the linear
solution. An example is studied to illuminate this point.Comment: 5 pages contributed to the proceedings "Loops and Legs 2004", April
2004, Zinnowitz, German
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