Asymptotic Quantum Dynamics of Ghost Fields

Abstract

The dressed propagator of a ghost coupled to ordinary fields develops a pair of complex conjugate poles in the first Riemann sheet above the multi-particle threshold. We study the implications of this pole structure for the asymptotic field and its negative-norm one-particle state. Within the operator formalism of local quantum field theory, we show that interactions between the ghost field and the composite field of the multi-particle state persist at asymptotic times. These induce quantum interference effects that render the negative-norm one-particle state non-orthogonal to, and thus indistinguishable from, a superposition of positive-norm multi-particle states. As a result, no free asymptotic one-particle ghost state exists. The real and imaginary parts of the complex mass admit a clear physical interpretation; in particular, the inverse imaginary part sets the timescale for the onset of non-orthogonality. A freely propagating ghost is therefore confined to time intervals much shorter than its inverse width, so that a detector can never observe an isolated ghost particle asymptotically. Open questions and potential applications are discussed in the conclusions.