Conformal invariant spinor theory with third-order derivatives

Abstract

It is demonstrated that a free Weyl spinor theory with third-order derivatives, which serves as an imbedding Lagrange theory for noncanonical spinor theories of the Heisenberg type, is not only scale invariant but invariant under the full 15-parameter conformal group. The spinor field transforms according to an irreducible representation for mass dimension 1/2. In a canonical formulation of this theory, in which the spin-projected first and second derivatives of the field are considered as independent dynamical variables, the new fields are found to transform according to nondecomposable representations for mass dimension 3/2 and 5/2, which produces nonconventional features. The special conformal currents are explicitly constructed in the third-order and canonical formalism and their conservation is demonstrated. Proposals for a conform invariant theory with interaction are made. It is shown to support a number of aspects of gauge-invariant spinor theories studied earlier. Conformal invariance leads to several new features in the case of interacting theories and, in connection with the occurrence of nondecomposable representations, brings to light the limitations of gauge replacement procedures for introducing interacting theories. The theory can be immediately generalized to Dirac-type spinor theories and theories with internal degrees of freedom.