A Supersymmetric Lagrangian for Fermionic Fields with Mass Dimension One

Abstract

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.

30 pages, added references

References in corpus (4)

• The Einstein-Cartan-Elko system
• The Einstein-Elko system -- Can dark matter drive inflation?
• The quadratic spinor Lagrangian, axial torsion current, and generalizations
• ELKO Spinor Fields: Lagrangians for Gravity derived from Supergravity

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• Questing for Algebraic Mass Dimension One Spinor Fields
• Elko and mass dimension one field of spin one half: causality and Fermi statistics
• On a local mass dimension one Fermi field of spin one-half and the theoretical crevice that allows it
• Dark matter, Elko fields and Weinberg's quantum field theory formalism
• Symmetries of Elko and massive vector fields
• The Lagrangian for mass dimension one fermionic dark matter
• Lagrangians for Massive Dirac Chiral Superfields