Classification of singular spinor fields and other mass dimension one fermions

Abstract

We investigate the constraint equations of the Lounesto spinor fields classification and show that it can be used to completely characterize all the singular classes, which can potentially accommodate further mass dimension one fermions, beyond the well known Elko spinor fields. This result can be useful for two purposes:besides a great abridgement in the classification of a given 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 spinors dynamics.

On the spinor representation

“…The general form of the spinors in each one of the above classes was derived in Refs. [18,28], and a classification that encodes gauge aspects was established in Ref. [29].…”

“…In fact, supposing the existence ofM such thatM 4 = D , then MM 4 = M 4 , leading to M = M −1 . Nevertheless, as it can be explicitly calculated from (28), det M = 0 and there is no such aM matrix. Secondly, the mapping (28) …”

Questing mass dimension 1 spinor fields

“…Such identities reduce the degrees of freedom to 7, being the extra degree of freedom associated to a phase factor. 2 Taking into account Eq. (15), it is usual, in order to reduce the degrees of freedom of Ψ , to define the following relation:…”

“…Moreover, with the aid of the boomerang it is possible likewise to prove that there are precisely six different classes of spinors in Lounesto's classification [1]. The most general forms of the respective spinors in each class were introduced in [2]. Lounesto's spinor classification was further employed to derive all the Lagrangians for gravity from the quadratic spinor Lagrangian [3].…”

Localization of five-dimensional Elko spinors with non-minimal coupling on thick branes

“…Hence the interactions between Elko spinor and gauge fields in SM will be suppressed strongly (at least one order of Plank scale), which means that Elko spinor only interacts with itself, graviton and Higgs fields [67][68][69][70][71][72][73][74][75]. Elko spinor has been considered as a first-principle candidate of dark matter [67][68][69][70][71] and has also been investigated extensively in cosmology [76][77][78][79][80][81][82][83][84][85] and mathematical physics [86][87][88][89][90][91][92].…”