Quantum Fields, Dark Matter, Elko Fields and Non-Standard Wigner Classes
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
In this thesis we examine the Elko field dark matter candidate, its interactions, and possible theoretical origins. We discuss important areas in which Elko Field Theory is incomplete and propose what we consider to be the most natural ways of plugging the holes in the theory. The way we propose to plug these holes enables Elko fields to interact with Standard Model gauge quanta. Any possible Elko darkness may be then due to Elko non-locality. The possible existence of Elko gauge interactions constitutes a significant result in this thesis. We also explore how Elko quantum fields might arise on the state space. We show that the Elko field is not a quantum field in the sense of Weinberg and that the Elko field violates the symmetries of the Lorentz group; another significant result altering how we think about Elko Field Theory. We also show that subgroups of the Lorentz group do not give rise to Elko fields (or their VSR counterparts) on the state space. We also examine the non-standard Wigner classes and show that in the context of our most natural ways of plugging the holes present in Elko Field Theory, Elko fields do not arise there either. We also show that in one of the non-standard Wigner classes, under certain conditions, there can exist a local massive spin-1/2 quantum field Majorana type dark matter candidate that is a well-defined quantum field in the sense of Weinberg. We give the dynamics of this new quantum field and also specify under what conditions this quantum field can exist. We finish the thesis by exploring Elko fields and their left and right-handed components in the context of the Electroweak Theory, in a more speculative way. We take the general concept of mass dimension transmutation introduced for Classical Spinor Theory by J.M. Hoff da Silva and R. da Rocha and apply it to the state space in the most natural way. We use this to derive a formula linking Dirac fields to the left-handed components of Elko fields and suggest the possibility of mass dimension transmutation being involved in electroweak interactions. Finally, we point out that although Elko fields cannot enter the Standard Model doublets, they can form their own doublets, the resulting symmetry currents of which can couple to the symmetry currents of the Standard Model.