Conformally and superconformally covariant equations for non-vanishing mass fields (Q1263743)

The conformal covariant theory was studied as early as in 1956 but it began attracting much attention only since 1969 with the discovery of the scaling invariant law in the process of inelastic interactions between leptons and hadrons. In recent time, conformally covariant equations have also been studied in the work by \textit{R. Kotecky} and \textit{J. Niederle} [Conformally covariant field equations, Czech. J. Phys. B 25, 123-149 (1975)] and \textit{J. Mickelsson} and \textit{J. Niederle} [Ann. Inst. Henri Poincaré, n. Ser., Sect. A 23, 277-295 (1975; Zbl 0313.53012)]. In the conformal covariant theory, one assumes that, under conformal transformations, the physical quantities are transformed according to their dimensions. Within the pure mathematical formalism this fact can be explained as follows: a conformal transformation is considered as a global or local transformation of measuring units, therefore measured values have to be transformed in an inverse proportion to the changes of the associated measuring units in order to ensure the invariance of the physical quantities. We use this interpretation for the transformation laws of the mass of fields under the conformal transformations.