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.
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Acknowledgments
GBG thanks FAPESP (2021/12126-5) for financial support and Dharam Vir Ahluwalia for his great scientific legacy. He dedicates this work to the memory of Dharam Vir Ahluwalia. JMHS thanks CNPq, Brazil for financial support through grant number 307641/2022-8. CYL thanks James Brister, Chou-Man Sou, Zheng Sun, Wenqi Yu and Siyi Zhou for useful discussions. CYL is supported by The Sichuan University Post-doctoral Research Fund No. 2022SCU12119. BMP thanks CNPq for partial support.
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ArXiv ePrint: 2312.17038
We are deeply saddened to have lost our beloved friend and long-time collaborator Dharam Vir Ahluwalia who has initiated and contributed so much to the theory of mass dimension one fields. His spirit will forever be with us.
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Ahluwalia, D.V., de Gracia, G.B., Hoff da Silva, J.M. et al. Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy. J. High Energ. Phys. 2024, 75 (2024). https://doi.org/10.1007/JHEP04(2024)075
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DOI: https://doi.org/10.1007/JHEP04(2024)075