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.