arXiv subjects
Publications and source records attributed to Dirk Kreimer.
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and report on recent results in support of this connection.
We investigate Feynman diagrams which are calculable in terms of generalized one-loop functions, and explore how the presence or absence of transcendentals in their counterterms reflects the entanglement of link diagram constructed from them and explains unexpected relations between them.
Work is reported on finite integral representations for 2-loop massive 2-, 3- and 4-point functions, using orthogonal and parallel space variables. It is shown that this can be utilized to cover particles with arbitrary spin (tensor integrals), and that UV divergences can be absorbed in an algebraic manner. This includes a classification of UV divergences by means of the topology of the graph, interpreted in terms of knots.
We give empirical evidence that the UV-divergences of a renormalizable field theory are knot invariants.
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
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.
We sketch a systematic approach to multiloop calculations. We focus on the Z-factors of a renormalizable theory and show that they can be obtained by purely algebraic methods based on power-counting and the forest structure of the divergent graphs. (submitted contributions to the conference proceedings "Confronting the Infinite", Adelaide February 1994)
We present a new method of calculating scalar propagator and vertex functions in the two-loop approximation, for arbitrary masses of particles. It is based on a double integral representation, suitable for numerical evaluation. Real and imaginary parts of the diagrams are calculated separately, so that there is no need to use complex arithmetics in the numerical program.
We discuss the consistency of a new \gf -scheme with renormalization. In particular we study the power-counting behaviour of multiloop graphs to prove its consistency. As a side effect we obtain a short proof of the Adler-Bardeen theorem. Further we show that this \gf-scheme does not modify the BRST identities at any loop orders in contrast to BM type schemes.
We give a new method for the reduction of tensor integrals to finite integral representations and UV divergent analytic expressions. This includes a new method for the handling of the gamma-algebra. TYPO IN EQUATION (5) CORRECTED, MACROS REORDERED.
We introduce in typical examples new methods for the calculation of massive loop integrals appearing in the radiative correction calculations of the Standard Model.