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We investigate the constraint equations of the Lounesto spinor fieldsclassification and show that it can be used to completely characterize all thesingular classes, which are potential accommodations for further mass dimensionone fermions, beyond the well known Elko spinor fields. This result can beuseful for two purposes: besides a great abridgement in the classification of agiven spinor field, we provide a general form of each class of spinor fields,which can be used furthermore to search for a general classification of spinorsdynamics.

Classification of Singular Spinor Fields and Other Mass Dimension One Fermions