Abstract
We demonstrate that the arbitrary-spin Bhabha fields with minimal electromagnetic coupling are causal in both the -number and -number theories. We first obtain the Klein-Gordon (KG) divisors in closed form in terms of the elementary symmetric functions. -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 -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 -number and -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.
- Received 15 September 1975
DOI:https://doi.org/10.1103/PhysRevD.13.924
©1976 American Physical Society