Inconsistency of the local field theory of charged spin 3/2 particles

Abstract

The relativistic quantum theory of Fermi Dirac fields of arbitrary spin is investigated and a general theorem is proved which aserts that for fields of half integral spin > ½, the possibility of a consistent quantization requires that the equal-time anticommutators must be functions of the other fields to which the field in question is coupled. The case of spin 3/2 is studied in detail and the equivalence of various formulations of the theory is shown. The inconsistency of the relativistic local quantum theory of a charged spin 3/2 field in interaction with an external electromagnetic field is demonstrated by showing that the equal time commutation relations and relativistic covariance of the theory are not compatible. Finally, the mixed spin 3/2-Spin ½ (Bhabha) field is found to be characterized by the same inconsistency.