Radiation of classical scalar fields from a point source: m → 0 limit of massive theory vs. m = 0 theory

Abstract

Radiation of a massive classical scalar field from a point source is studied in the mass zero limit and compared with the radiation emitted in a mass zero theory. The total radiated energy momentum is the same in both theories, but the rate cannot be got in the massive theory. The massive theory admits a particle number-probability interpretation, and a speed distribution and energy distribution can be found. The energy distribution goes like ω −(2 n+1) at high energies, the value of n depending on smoothness properties of the source world line. In the low ω region it is proportional to ω −1 until (ω − m) m ⪡ 1 , where a strong suppression factor proportional to ν 2 dominates. But despite this fact the radiated number diverges like log m −1 owing to contributions from particles with energies O( m 0) but with ultrarelativistic speeds. Other interesting features have to do with speed distribution properties in the m → 0 case.