Now, suppose that A ^ ^ is an annihilation operator. To move A ^ ^ from the left-hand side to the right-hand side of all the products, we repeatedly swap A ^ ^ with the operator immediately right of it (call it X ^ ^ ), each time applying A ^ ^ X ^ ^ = : A ^ ^ X ^ ^ : + A ^ ^ ∙ ∙ X ^ ^ ∙ ∙ to account for noncommutativity. Once we do this, all terms will be normal ordered. All terms added to the sums by pushing A ^ ^ through the products correspond to additional contractions involving A ^ ^ . Therefore, if A ^ ^ is an annihilation operator, Wick's theorem holds for A ^ ^ B ^ ^ C ^ ^ D ^ ^ E ^ ^ F ^ ^ … … .