We present the derivation of a supersymmetric model for fermionic fields with integer-valued mass dimension based on a general superfield with one free spinor index. First, we develop a formalism based on a general superfield with one free spinor index. Then, we systematically derive all associated chiral and antichiral superfields up to third order in covariant derivatives. Using this formalism we are able to construct a supersymmetric on-shell Lagrangian that contains a kinetic term for the fermionic fields with mass dimension one. We then derive the corresponding on-shell supercurrent and succeed in formulating a consistent second quantisation for the component fields. Finally, we present our result for a supersymmetric Hamiltonian. As the Lagrangian is by construction supersymmetric and the Hamiltonian was derived from the Lagrangian using supersymmetry algebra the Hamiltonian must be positive definite.
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