We investigate the nonperturbative quantization of phantom and ghost degrees of freedom by relating their representations in definite and indefinite inner product spaces. For a large class of potentials, we argue that the same physical information can be extracted from either representation. We provide a definition of the path integral for these theories, even in cases where the integrand may be exponentially unbounded, thereby removing some previous obstacles to their nonperturbative study. We apply our results to the study of ghost fields of Pauli–Villars and Lee–Wick type, and we show in the context of a toy model how to derive, from an exact nonperturbative path integral calculation, previously ad hoc prescriptions for Feynman diagram contour integrals in the presence of complex energies. We point out that the pole prescriptions obtained in ghost theories are opposite to what would have been expected if one had added conventional i∊ convergence factors in the path integral.
Using the complex coordinate method, it is possible to compute the physical properties of atomic resonances above the ionization threshold. We show how to define and compute the electronic densities associated with these atomic resonances. The method is general and is illustrated for atomic Rydberg states in static and time-dependent external fields.