Meromorphic germs (say at zero) in several variables with linear poles naturally arise in the context of renormalisation, which calls for a method to evaluate them at the poles. A first step is to write the meromorphic germ as a sum of a holomorphic part and a polar part, which requires a splitting device. We shall show how a locality relation on meromorphic germs reminiscent of locality in QFT does the job in that it enables us to build a multi-variable Laurent expansion. This in turn yields a minimal subtraction scheme in several variables which respects locality. We further consider transformations on meromorphic germs that preserve locality while leaving the holomorphic germs invariant and the resulting Galois group.
The aim of the talk is to show how on certain natural classes of meromorphic germs with a prescribed type of linear pole, any other evaluator which extends the ordinary evaluation at zero on holomorphic germs and preserves locality, amounts to a minimal subtraction scheme modulo a Galois type transformation.
This talk is based on joint work with Li Guo and Bin Zhang.