Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy
Abstract Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-04-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2024)075 |
| _version_ | 1827176254054334464 |
|---|---|
| author | Dharam Vir Ahluwalia G. B. de Gracia Julio M. Hoff da Silva Cheng-Yang Lee B. M. Pimentel |
| author_facet | Dharam Vir Ahluwalia G. B. de Gracia Julio M. Hoff da Silva Cheng-Yang Lee B. M. Pimentel |
| author_sort | Dharam Vir Ahluwalia |
| collection | DOAJ |
| description | Abstract Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these to creation and annihilation operators in a specific manner. This is implicit in his implementation of the rotational symmetry for the spin half quantum field. Among the numerous complete set of spinors that are available to a physicist, Elko occupies a unique status that allows it to enter as expansion coefficients of a quantum field without violating Weinberg’s no go theorem. How this paradigm changing claim arises is the primary subject of this communication. Weinberg’s no go theorem is evaded by exploiting a uniquely special feature of Elko that allows us to introduce a doubling of the particle-antiparticle degrees of freedom from four to eight. Weinberg had dismissed this degeneracy on the ground that, “no examples are known of particles that furnish unconventional representations of inversions.” Here we will find that this degeneracy, once envisioned by Eugene Wigner, in fact gives rise to a quantum field that has all the theoretical properties required of dark matter. |
| first_indexed | 2024-04-24T09:57:02Z |
| format | Article |
| id | doaj.art-cd18e447606b42038803fa4515cefc06 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2025-03-21T04:24:25Z |
| publishDate | 2024-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-cd18e447606b42038803fa4515cefc062024-07-28T11:05:52ZengSpringerOpenJournal of High Energy Physics1029-84792024-04-012024413810.1007/JHEP04(2024)075Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracyDharam Vir Ahluwalia0G. B. de Gracia1Julio M. Hoff da Silva2Cheng-Yang Lee3B. M. Pimentel4Center for the Studies of the Glass Bead GameFederal University of ABC, Center of MathematicsDepartamento de Fisica, Univeridade Estadual Paulista, UNESPCenter for Theoretical Physics, College of Physics, Sichuan UniversityInstitute of Theoretical Physics, Sao Paulo State UniversityAbstract Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these to creation and annihilation operators in a specific manner. This is implicit in his implementation of the rotational symmetry for the spin half quantum field. Among the numerous complete set of spinors that are available to a physicist, Elko occupies a unique status that allows it to enter as expansion coefficients of a quantum field without violating Weinberg’s no go theorem. How this paradigm changing claim arises is the primary subject of this communication. Weinberg’s no go theorem is evaded by exploiting a uniquely special feature of Elko that allows us to introduce a doubling of the particle-antiparticle degrees of freedom from four to eight. Weinberg had dismissed this degeneracy on the ground that, “no examples are known of particles that furnish unconventional representations of inversions.” Here we will find that this degeneracy, once envisioned by Eugene Wigner, in fact gives rise to a quantum field that has all the theoretical properties required of dark matter.https://doi.org/10.1007/JHEP04(2024)075Space-Time SymmetriesDiscrete Symmetries |
| spellingShingle | Dharam Vir Ahluwalia G. B. de Gracia Julio M. Hoff da Silva Cheng-Yang Lee B. M. Pimentel Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy Journal of High Energy Physics Space-Time Symmetries Discrete Symmetries |
| title | Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy |
| title_full | Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy |
| title_fullStr | Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy |
| title_full_unstemmed | Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy |
| title_short | Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy |
| title_sort | irreducible representations of the poincare group with reflections and two fold wigner degeneracy |
| topic | Space-Time Symmetries Discrete Symmetries |
| url | https://doi.org/10.1007/JHEP04(2024)075 |
| work_keys_str_mv | AT dharamvirahluwalia irreduciblerepresentationsofthepoincaregroupwithreflectionsandtwofoldwignerdegeneracy AT gbdegracia irreduciblerepresentationsofthepoincaregroupwithreflectionsandtwofoldwignerdegeneracy AT juliomhoffdasilva irreduciblerepresentationsofthepoincaregroupwithreflectionsandtwofoldwignerdegeneracy AT chengyanglee irreduciblerepresentationsofthepoincaregroupwithreflectionsandtwofoldwignerdegeneracy AT bmpimentel irreduciblerepresentationsofthepoincaregroupwithreflectionsandtwofoldwignerdegeneracy |