Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions
Abstract 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 $${\mathcal {Z}}(z)$$ Z ( z ) where z is a complex number. The theory is non-local and non-covariant. While i...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-01-01
|
| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-021-08860-z |
| _version_ | 1818622693110448128 |
|---|---|
| author | Cheng-Yang Lee |
| author_facet | Cheng-Yang Lee |
| author_sort | Cheng-Yang Lee |
| collection | DOAJ |
| description | Abstract 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 $${\mathcal {Z}}(z)$$ Z ( z ) 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 $$\tau $$ τ -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 $$|z|\ne 1$$ | z | ≠ 1 and $$|z|=1$$ | z | = 1 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. |
| first_indexed | 2024-12-16T18:29:13Z |
| format | Article |
| id | doaj.art-9ecc7fe909884f2ca0379d9fea0aa7d3 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-16T18:29:13Z |
| publishDate | 2021-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-9ecc7fe909884f2ca0379d9fea0aa7d32022-12-21T22:21:21ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522021-01-018111810.1140/epjc/s10052-021-08860-zFermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermionsCheng-Yang Lee0Manipal Centre for Natural Sciences, Centre of Excellence, Manipal Academy of Higher EducationAbstract 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 $${\mathcal {Z}}(z)$$ Z ( z ) 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 $$\tau $$ τ -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 $$|z|\ne 1$$ | z | ≠ 1 and $$|z|=1$$ | z | = 1 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.https://doi.org/10.1140/epjc/s10052-021-08860-z |
| spellingShingle | Cheng-Yang Lee Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions European Physical Journal C: Particles and Fields |
| title | Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions |
| title_full | Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions |
| title_fullStr | Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions |
| title_full_unstemmed | Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions |
| title_short | Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions |
| title_sort | fermionic degeneracy and non local contributions in flag dipole spinors and mass dimension one fermions |
| url | https://doi.org/10.1140/epjc/s10052-021-08860-z |
| work_keys_str_mv | AT chengyanglee fermionicdegeneracyandnonlocalcontributionsinflagdipolespinorsandmassdimensiononefermions |