(Received October 24, 1963)
The quantized field of unstable particles without charge and spin is introduced. With this purpose, c-number solutions of the Klein-Gordon equation with complex mass m = m0 - (i/2)γ are investigated, and it is proved that a new set of non-scalar elementary wave solutions, which represent a direct idealization of states of a freely moving unstable particle, exists for the values of γ/2m0 smaller than the critical value which is evaluated to be 0.8 … With the aid of this set of elementary wave solutions, the quantized free unstable particle field is defined mathematically well. The commutator of the fields is evaluated, which turns out to be an invariant function of coordinates-difference in spite of the non-simple transformation property of the elementary waves used, and vanishes for the space-like separations. The resulting causal Green function ΔF has a good asymptotic behaviour at large distances. The set of infinitesimal generators of the inhomogeneous Lorentz group is found in terms of the creation and annihilation operators of particles, and it is shown that there exists a representation which is non-unitary, of the inhomogeneous Lorentz group. The quantized field and the generators, Pµ and Mµν have no simple transformation property like scalar, vector and tensor.
URL :
http://ptp.ipap.jp/link?PTP/31/269/
DOI : 10.1143/PTP.31.269