Bhabha first-order wave equations. IV. Causality with minimal electromagnetic coupling

It is demonstrated that the arbitrary-spin Bhabha fields with minimal electromagnetic coupling are causal in both the c-number and q-number theories. The Klein-Gordon (KG) divisors in closed form are first obtained in terms of the elementary symmetric functions. c-number causality is easily demonstrated for half-integer spin with the Velo-Zwanziger method and integer spin by using Wightman's suggestion involving the KG divisors. For the q-number demonstration, an indefinite-metric second-quantized formalism is set up, and the above KG divisors are used 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. Discussion focuses on the Bhabha indefinite metric and on the connection between the number of derivatives in a theory and the occurrence or nonoccurence of causality