A NEW QUANTUM NUMBER DERIVED FROM CONFORMAL INVARIANCE

A detailed analysis of the conformal group of relativistic space-time and its four-dimensional homogeneous spaces shows that for example the mass 0 scalar field in the appropriate (not the usual) conformal compactification of Minkowski space carries a unitary representation not of the conformal group SOO(4.2)/C2. but of its covering group SOO(4.2). The invariant definition of causality is given. and the representations to mass 0 of the spin-covering group SUO(2,2) of the conformal group are investigted. The physical consequences are either the existence of a new conserved multiplicative quantum number R for conformal symmetry (the corresponding selection rule would for example forbid the process spin 0 → 2γ for mass 0 particles). or the prediction that all possible mass 0. spin |s| ≤ 2 particles are given by the γ-quantum. one type of neutrino (the left-handed for example). and a spin 3 2 particle whose helicity has the opposite sign. © 1969.