Weyl composition of symbols in large dimension

This paper is concerned with the Weyl composition of symbols in large dimension. We specify a class of symbols in order to estimate the Weyl symbol of the product of two Weyl $h-$pseudodifferential operators, with constants independent of the dimension. The proof includes a regularized and a hybrid compositions together with a decomposition formula. We also analyze in this context the remainder term of the semiclassical expansion of the Weyl composition.