Radiation from an emitter in the ghost free scalar theory

TL;DR

This paper investigates how ghost-free modifications of scalar field theory affect radiation emitted by a point-like, monochromatic source, revealing that near the source the field exhibits oscillatory behavior and potential pathologies.

Contribution

It provides a detailed analysis of radiation in ghost-free scalar theories, highlighting differences from classical theory and identifying possible pathological behaviors.

Findings

Far from the source, radiation converges to classical values for all N.

Near the source, the field shows oscillations with amplitude depending on N.

For even N, oscillation amplitude remains finite; for odd N, it grows infinitely with frequency.

Abstract

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 focused on the most common versions of the ghost-free theory, where the propagator $\Box^{-1}$ is modified as follows $\exp(-(\Box/\mu^2)^N) \Box^{-1}$, where $\mu$ is the characteristic mass-scale of such $GF_N$-theory. We demonstrated that far from the source, in the wave-zone, the radiation asymptotically converges to its "classical" value for any $N\ge 1$. However, in the near-zone the behavior of the field is quite different from the "classical" case. The difference of field amplitude for the ghost-free field and for the classical one has an oscillatory behavior in this domain. A number of oscillations increases with $N$. The amplitude of these oscillations remain finite for even $N$, while it infinitely grows with frequency for odd $N$. This behavior indicates that even in the classical domain $GF_N$ theories might have pathological behavior.