Conformal symmetry in the Bhabha theory

Abstract

The first-order formalism of relativistic wave equations, such as the Dirac (spin s = 1=2) and the Kemmer (s = 1) equations, are generalized to the Bhabha (one s) equation, where the generalized gamma matrices for space-time dimension (3+1) are labeled with not only s but also s′ ∈ {s, s − 1,… s − ⎣s⎦}. We show that for s′ = s, the generators (D, Pμ , Kμ , Sμν ) constructed from the generalized gamma matrices satisfy the conformal algebra, in which we find that the null-eigenstates |s ±〉 with respect to Pμ and Kμ as Pμ |s +〉 = 0 = Kμ |s −〉 have the two following properties: the dimension of the eigenspace for|s ±〉 is given by 2s + 1, and , where represents the spin magnitude. In this sense, we can regard |s ±〉 as physical states for a massive particle.