Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-10-05
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, added references
Scientific paper
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 demonstrate that it is impossible to formulate such a model based on a general scalar superfield. This is due to problems constructing a Lagrangian containing a kinetic term for the fermionic mass dimension one field, as well as problems deriving a consistent second quantisation. We then develop a formalism based on a general superfield with one free spinor index. We systematically derive all associated chiral and anti-chiral 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 to formulate 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 the supersymmetry algebra the Hamiltonian must be positive definite.
Dick Rainer
Wunderle Kai E.
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