  The one-dimensional transverse field Ising model is solved by continuous
unitary transformations in the high-field limit. A high accuracy is reached due
to the closure of the relevant algebra of operators which we call string
operators. The closure is related to the possibility to map the model by
Jordan-Wigner transformation to non-interacting fermions. But it is proven
without referring to this mapping. The effective model derived by the
continuous unitary transformations is used to compute the contributions of one,
two, and three elementary excitations to the diagonal dynamic structure
factors. The three-particle contributions have so far not been addressed
analytically, except close to the quantum critical point.
