We investigate the possibility that the dimension 2 condensate A 2 µ 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 renormalisable, 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 renormalisability up to three loops and secondly to the Coleman-Weinberg model where gauge independence of the effective potential for the local composite operator φφ * is explicitly checked up to two loops.

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.Comment: 10 page