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 ^-1 is modified as follows: exp(-(/μ²)N)^-1, where μ is the characteristic mass scale of such a GFN theory. We demonstrate that far from the source, in the wave zone, the radiation asymptotically converges to its ``classical'' value for any N≥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 GFN theories might have pathological behavior.