Eigenstates of boson creation operator

We examine the existence of right-hand eigenstates (or eigenkets) of the bo son creation operator a(dagger) and determine their coordinate and their Ba rgmann representation. The eigenkets of the creation operator are ultrasing ular and cannot be considered as a limiting case of normalizable states. Ap plications of these eigenstates as auxiliary states for purposes of represe ntation of states by path integrals over coherent states are discussed. A c ompleteness relation for coherent states on paths through the complex plane is derived and special examples of its application are considered.