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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 w-'~~+I) at high energies, the value of n depending on smoothness properties of the source world line. In the low w region it is proportional to w-l until ( w -m)/m < 1, where a strong suppression factor proportional to V" dominates. But despite this fact the radiated number diverges like log mm1 owing to contributions from particles with energies O(mO) but with ultrarelativistic speeds. Other interesting features have to do with speed distribution properties in the m + 0 case.
Generating Functional and Green's Function Hierarchy of the Ising Model. F. SCHWABI..
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