Hermitian formulation for mass dimension one fermions: Flat and curved spacetimes Gabriel Brandão de Gracia, Rodolfo José Bueno Rogerio Modern Physics Letters A, 2025 Throughout this paper, we conduct our discussion by a partial review of [G. B. de Gracia et al., Phys. Dark Universe 47, 101774 (2025)], introducing the Hermitian formulation for interacting mass dimension one fermions based on Elko spinor. It includes pivotal observations about renormalizability and the study of some allowed interactions. Beyond these points, since dark-matter phenomenology is mainly connected to gravitation, we introduce original remarks on how the Hermitian prescription can be readily generalized to include curved spacetime, considering the very definition of the Elko spinor structure. We establish the Elko dual as arising from the path-integral formulation of a more fundamental structure. It enables one to include a curved background spacetime and also quantum gravity into our investigations. Dharam’s rare blend of audacity, integrity, and brilliance reshaped how we think and aspire in science.
Pseudoclassical mechanics à la Faddeev-Jackiw L. G. Caro, G. B. de Gracia, B. M. Pimentel, G. E. R. Zambrano International Journal of Modern Physics A, 2024 In this study, we propose an extension of the formulation developed by Faddeev and Jackiw to include anticommutative variables in the language of supergeometry, as it could be a cost-effective way to determine the ([Formula: see text]-graded) Poisson structure of theories describing spin-like degrees of freedom. Specifically, we apply the developed approach to pseudoclassical systems to lately use the standard canonical quantization program to check whether their already known quantum description is recovered.
Irreducible representations of the Poincaré group with reflections and two-fold Wigner degeneracy Dharam Vir Ahluwalia, G. B. de Gracia, Julio M. Hoff da Silva, Cheng-Yang Lee, B. M. Pimentel Journal of High Energy Physics, 2024 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.
