COORDINATE COVARIANCE AND THE PARTICLE SPECTRUM

An attempt is made to find an analog, for the quantum mechanics of non- Euclidean space-time, to the classification of representations of the Lorentz group. The difficulty of obtaining any such classification in terms of curvilinear coordinates is pointed out, and the use of a higherdimensional set of pseudo-Euclidean coordinates is chosen as an alternative mode of classification. A class of representations then follow easily. On the basis of an intuitive approximation it is found that spectra of elementary particles, with conservation of quantities of the nature of isotopic spin, seem to arise from these representations. (auth)