Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-24
Physics
High Energy Physics
High Energy Physics - Theory
An overlooked similarity transformation makes the result trivial (hence the pre-print is withdrawn)
Scientific paper
It is well known that both the Dirac and Majorana quantum fields have Dirac spinors as their expansion coefficients. In 2005 Ahluwalia and Grumiller introduced a complete set of eigenspinors of the charge conjugation operator, and extended the notion of Majorana spinors to Elko. This work not only shed new light on Majorana field and Majorana spinors, but revealed new physical and mathematical contents resulting from the Elko extension. It is now known that Elko, and hence Majorana spinors, have a built-in violation of the Lorentz symmetry and carry a well defined element of non-locality. This has far reaching consequences for theories that rely on these spinors. All these results apply in 3+1 dimensions. Here, we show that, in 1+1 dimensions, the Elko fields constructed from Elko spinors are local and satisfy the symmetry of a subgroup of the Poincar\'{e} group. The fields in 1+1 dimensions are of mass dimension one-half and have Dirac-like Lagrangians with renormalisable self-coupling terms similar to those of the the Thirring model.
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