Radiation from an emitter in the ghost free scalar theory

We study radiation emitted by a time-dependent source of a scalar massless field in the framework of the ghost-free modifications of the theory. We consider a simple model of the emitter: namely, we assume that it is point-like and monochromatic. We focus on the most common versions of the ghost-free theory, where the propagator ${\ensuremath{\square}}^{\ensuremath{-}1}$ is modified as follows: $\mathrm{exp}(\ensuremath{-}(\ensuremath{\square}/{\ensuremath{\mu}}^{2}{)}^{N}){\ensuremath{\square}}^{\ensuremath{-}1}$, where $\ensuremath{\mu}$ is the characteristic mass scale of such a $G{F}_{N}$ theory. We demonstrate that far from the source, in the wave zone, the radiation asymptotically converges to its ``classical'' value for any $N\ensuremath{\ge}1$. However, in the near zone the behavior of the field is quite different from the ``classical'' case. The difference of the field amplitude for the ghost-free field and for the classical one has an oscillatory behavior in this domain. The number of oscillations increases with $N$. The amplitude of these oscillations remains finite for even $N$, while it infinitely grows with frequency for odd $N$. This behavior indicates that even in the classical domain $G{F}_{N}$ theories might have pathological behavior.

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