arXiv subjects
Publications and source records attributed to K. Knecht.
Tensor reduction of vacuum diagrams uses contraction and decomposition matrices. We present general recurrence relations for the calculation of those matrices and an explicit formula for the 3-loop decomposition matrix and its determinant.
We investigate the possibility that the dimension 2 condensate A_mu^2 has a non zero non-perturbative value in Yang-Mills theory. We introduce a multiplicatively renormalisable effective potential for this condensate and show through two loop calculations that a non zero condensate is energetically favoured.
We present a formalism for local composite operators. The corresponding effective potential is unique, multiplicatively renormalizable, it is the sum of 1PI diagrams and can be interpreted as an energy-density. First we apply this method to $λΦ^4$ theory where we check renormalizability up to three loops and secondly to the Coleman-Weinberg model where the gauge independence of the effective potential for the local composite operator $ϕϕ^*$ is explicitely checked up to two loops.
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a representation consisting of well-defined compact integrals. The result is a simple transformation of the integrand which gives the analytic continuation of a wide class of Feynmanintegrals. The algorithm will especially be fit for numerical calculation of general massive multi-loop integrals. An important advantage of this method is that it allows us to calculate both infinite and finite parts independently.