  We present a fermion model characterized by an anticommuting-parameter shift
symmetry. The Hamiltonian formulation exhibits a combination of first-class and
second-class constraints. We derive the well-known Dirac equation by fixing the
gauge in a covariant manner, enabling the fields to propagate accordingly.
Notably, the model inherently possesses invariance under reparametrizations of
time. Consequently, the Hamiltonian vanishes, setting it apart from the
conventional framework of Dirac's theory. Furthermore, we establish a
correspondence between these particles and the zero-modes of the massless
Rarita-Schwinger system, bringing forth the intriguing implication that they
may describe a supergravity ground state.
