Benjamin Martin

Dark Matter, Elko Fields and Weinberg's Quantum Field Theory Formalism

The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Wembergs formalism for quantum field theory. We prove that if one takes the symmetry group to be the full Pomcare group then the Elko field is not a quantum field in the sense of Weinberg. This confirms results of Ahluwalia, Lee and Schritt, who showed using a different approach that the Elko field does not transform covariantly under rotations and hence has a preferred axis.

G-complete reducibility in non-connected groups

The authors acknowledge the financial support of the DFG-priority programme SPP1388 “Representation Theory” and Marsden Grants UOC0501, UOC1009 and UOA1021. Part of the research for this paper was carried out while the authors were staying at the Mathematical Research Institute Oberwolfach supported by the “Research in Pairs” programme. The second author acknowledges additional support from ERC Advanced Grant No. 291512. The authors are grateful to the referee for helpful suggestions, including a strengthening of Proposition 3.4.