Gauge and time-reparametrization invariant spin-half fields

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