Regular Article - Theoretical Physics
Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions
Manipal Centre for Natural Sciences, Centre of Excellence, Manipal Academy of Higher Education, Dr. T. M. A. Pai Planetarium Building, 576104, Manipal, Karnataka, India
2 Center for Theoretical Physics, College of Physical Science and Technology, Sichuan University, 610064, Chengdu, China
Accepted: 11 January 2021
Published online: 27 January 2021
We construct a mass dimension one fermionic field associated with flag-dipole spinors. These spinors are related to Elko (flag-pole spinors) by a one-parameter matrix transformation where z is a complex number. The theory is non-local and non-covariant. While it is possible to obtain a Lorentz-invariant theory via -deformation, we choose to study the effects of non-locality and non-covariance. Our motivation for doing so is explained. We show that a fermionic field with and are physically equivalent. But for fermionic fields with more than one value of z, their interactions are z-dependent thus introducing an additional fermionic degeneracy that is absent in the Lorentz-invariant theory. We study the fermionic self-interaction and the local U(1) interaction. In the process, we obtained non-local contributions for fermionic self-interaction that have previously been neglected. For the local U(1) theory, the interactions contain time derivatives that renders the interacting density non-commutative at space-like separation. We show that this problem can be resolved by working in the temporal gauge. This issue is also discussed in the context of gravity.
© The Author(s) 2021
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