Spinor fields invariant under space–time transformations

Abstract

Spinor fields invariant under the subgroups of the Poincaré group or under the maximal subgroups of the conformal group of space–time are analyzed. It is shown that only certain Poincaré subgroups, all of dimension less than or equal to six, can leave two component spinor fields invariant, with rather severe restrictions on the fields. Tables listing all such invariant fields for subgroups of dimension greater than or equal to four are given. Construction of Dirac spinors and connections between invariant spinors and tensors are discussed: In particular it is shown that from any two-component spinor invariant under a Poincaré subgroup a real skew-symmetric tensor invariant under the same group may be constructed.