A new local gauge symmetry associated with the little groups of the four-velocity and the Pauli-Lubanski spin vector

It is shown that the (quantum or classical) observables for a spin-12 massive electron are invariant under a local one-parameter group of gauge transformation whose generator is dependent on the fermion “fields” of the theory, as well as conventional (constant) Lie algebra generators. This one-parameter family of local transformations is 2 → 1 homomorphic to a set of operators common to both the “little group” of the four-velocity and the “little group” of the Pauli-Lubanski spin vector. This symmetry is called the “little symmetry” to emphasize its connection to Wigner’s “little group.” The physical origin of this “little symmetry” is discussed. Typeset using REVTEX 1