Bhabha first-order wave equations. iv. causality with minimal electromagnetic coupling

Abstract

We demonstrate that the arbitrary-spin Bhabha fields with minimal electromagnetic coupling are causal in both the $c$-number and $q$-number theories. We first obtain the Klein-Gordon (KG) divisors in closed form in terms of the elementary symmetric functions. $c$-number causality is easily demonstrated for half-integer spin with the Velo-Zwanziger method and for integer spin by using Wightman's suggestion involving the KG divisors. For the $q$-number demonstration we set up an indefinite-metric second-quantized formalism, and use the above KG divisors to show causality in closed form for arbitrary spin. In both the $c$-number and $q$-number theories a special handling of the integer-spin subsidiary components is necessary. Our discussion focuses on the Bhabha indefinite metric and on the connection between the number of derivatives in a theory and the occurrence or nonoccurrence of causality.