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J. M. Hoff da Silva

Publications and source records attributed to J. M. Hoff da Silva.

At least 19 recordsLinked to original sources
arXiv2026

Topologically induced deformations of differential forms

Motivated by deformations of spin structures and their geometric implications, we study a deformed exterior derivative, which is a third-order nilpotent operator. This higher-order differential structure induces an anholonomic rescaling of the local frame and leads to a bifurcation of the associated cohomological structure, with two distinct notions of closedness and exactness. We prove that the Poincaré Lemma fails in both sectors, so that closed deformed forms need not be exact even locally. We then apply the resulting framework to a four-dimensional effective field theory and show that a constant saturation of the deformation parameter can generate a hierarchy between the electroweak and fundamental Planck scales through a purely geometric mechanism, without introducing extra spatial dimensions.

hep-th↗
arXiv2026

$\mathrm{ISIM}(2)$ gravitational gauge model via Soft Algebra formalism

This work presents a comprehensive account of a gravitational model based on the gauging of the $\mathrm{ISIM}(2)$ Lorentz subgroup parameters through the so-called soft algebra formalism. After presenting a closed form for $\mathfrak{sim}(2)$ and its inhomogeneous extension, we proceed to develop a complete torsionless gravitational model, culminating in an invariant action.

gr-qc↗
arXiv2026

Notes on obstructions in the hyperbolic Clifford algebra bundle structure

Starting from a general analysis of obstruction classes, we develop the investigation of obstructions associated with the bundle structure of the hyperbolic Clifford algebra. By taking into account particularities arising from the Whitney sum, it is shown that, unlike classical tangent bundle cases, the hyperbolic frame bundle admits lifting without any topological obstruction. This leads to the possibility of always defining spinor structures in hyperbolic Clifford bundles.

math-ph↗
arXiv2026

From Lorentz to $SIM(2)$: contraction, four-dimensional algebraic relations and projective representations

We present a comprehensive study on $SIM(2)$ and $ISIM(2)$ groups, their representations and algebraic aspects. These groups, together with $HOM(2)$, arise as the symmetry groups of Very Special Relativity (VSR), where full Lorentz invariance is reduced while retaining many relativistic consequences. After obtaining $SIM(2)$ through the Inönü-Wigner contraction procedure, a complete four-dimensional algebraic representation is shown for $\mathfrak{sim(2)}$ and $\mathfrak{isim(2)}$. Besides that, we apply Bargmann's formalism to investigate the (projective) representations for both cases, keeping track of the source of phase factors. We complete the study by presenting a particularly simple analysis to probe the existence of local phase factors, which is useful when dealing with non-abelian groups.

math-ph↗
arXiv2025

A unified approach to spinor duals via Clifford algebras and $G_Ω$ groups

Recent developments in the construction of generalized Dirac duals have revealed, within the structure of the Clifford algebra $\mathbb{C}\otimes\mathcal{C}\ell_{1,3},$ the existence of distinct algebraic formulations of spinors duals with potential applications in quantum field theoretic models. In this work, after reviewing the matrix formulation, we employ the recent covariant formulation of the generalized spinor dual and establish its interplay with the algebra $\mathcal{C}\ell_{1,3}$. We construct dual mappings governed by groups denoted by $G_Ω$ and introduce the notion of $Ω$-equivalence classes as a tool to classify dual spinors from a group-theoretic perspective.

math-ph↗
arXiv2025

Breaking the permutation character of diffeomorphisms on spinor structures

We investigate the impact of diffeomorphisms where more than one nonequivalent spinor structure is built upon a given base manifold endowed with nontrivial topology. We call attention to the fact that a relatively straightforward construction evinces a lack of symmetry between fermionic modes from different spinor bundle sections, leading to a dynamic preference breaking the permutation character of diffeomorphisms on spinor structures.

math-ph↗
arXiv2025

Foundational aspects of spinor structures and exotic spinors

Spinors are mathematical objects susceptible to the spacetime characteristics upon which they are defined. Not all spacetimes admit spinor structure; when it does, it may have more than one spinor structure, depending on topological properties. When more than one nonequivalent spinor structure is allowed in a given spacetime, the spinors resulting from the extra structures are called exotic. In this review, we revisit the topological conditions driving the discussion about the spacetime characteristics leading to the existence and (non)uniqueness of spinor structures in a relatively comprehensive manner, accounting for step-to-step demonstrations. In the sequel, we delve into the topologically corrected Dirac operator, explicitly obtaining it and exploring the physical consequences encoded in the exotic spinor dynamics. Finally, we overview early and recent achievements in the area, pointing out possible directions within this research program.

math-ph↗
arXiv2025

Deformations in spinor bundles: Lorentz violation and further physical implications

This paper delves into the deformation of spinor structures within nontrivial topologies and their physical implications. The deformation is modeled by introducing real functions that modify the standard spinor dynamics, leading to distinct physical regions characterized by varying degrees of Lorentz symmetry violation. It allows us to investigate the effects in the dynamical equation and a geometrized nonlinear sigma model. The findings suggest significant implications for the spinor fields in regions with nontrivial topologies, providing a robust mathematical approach to studying exotic spinor behavior.

math-ph↗
arXiv2024

A note on hidden classes in spinor classification

The Lounesto classification is a well-established scheme for categorizing spinors based on their physical content, which are determined by their associated bilinear forms. It consists of six disjoint classes encompassing the known spinors within the context of the standard model of high-energy physics. However, advancements in theories beyond the standard model have opened the door to potential new spinorial adjoint structures, leading to new unforeseen classess. These developments indicate the potential for extending the standard Lounesto classification. In this paper, we explore all possible subclasses that could extend the Lounesto scheme. We highlight the most relevant subclasses by imposing constraints to their corresponding dual structures, thus broadening our understanding of spinor and its applications in theoretical physics.

math-ph↗
arXiv2024

Emergent spinor fields from exotic spin structures

The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping the underlying spacetime with an extended bilinear form with additional terms coming from the nontrivial topology, naturally yield emergent extended algebraic spinor fields and their subsequent extended bilinear covariants, which are contrasted to the classical spinor classification. An unexpected duality between the standard and the exotic spinor field classes is therefore established, showing that a complementary fusion process among the spinor field classes sets in, when extended Clifford bundles are addressed in multiply-connected spacetimes.

hep-th↗
arXiv2023

Non-standard Wigner doublets

Guided by a conservative formulation in investigating the physical content of quantum fields, we explore non-standard Wigner classes of particles that could provide the basis for self-interaction models to dark matter. We critically contrast the analysis with long-standing constraints to non-standard Wigner classes in the literature to discuss the model's viability.

hep-th↗
arXiv2023

Local versus global subtleties of projective representations

In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main necessary theorems. We discuss the implementation of useful algebraic topology tools to characterize representations.

math-ph↗
arXiv2023

Perturbative aspects of mass dimension one fermions non-minimally coupled to electromagnetic field

This paper addresses perturbative aspects of the renormalization of a fermion with mass dimension one non-minimally coupled to the electromagnetic field. Specifically, we calculate the one-loop corrections to the propagators and vertex functions of the model and determine the one-loop beta function of the non-minimal electromagnetic coupling. Additionally, we perform calculations of the two-loop corrections to the gauge field propagator, demonstrating that it remains massless and transverse up to this order. We also find that the non-minimal electromagnetic coupling can exhibit asymptotic freedom if a certain condition is satisfied. As a potential dark matter candidate, these findings suggest that the field may decouple at high energies. This aspect holds significance for calculating the relic abundance and freeze-out temperature of the field, particularly in relation to processes involving the ordinary particles of the Standard Model.

hep-ph↗
arXiv2023

Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks

The so-called Takahashi's \emph{Inversion Theorem}, the reconstruction of a given spinor based on its bilinear covariants, are re-examined, considering alternative dual structures. In contrast to the classical results, where the Dirac dual structure plays the central role, new duals are built using the discrete symmetries $\mathcal{C}, \mathcal{P}, \mathcal{T}$. Their combinations are also taken into account. Furthermore, the imposition of a new adjoint structure led us also to re-examine the representation of the Clifford algebra basis elements, uncovering new bilinear structures and a new Fierz aggregate. Those results might help construct theories for new beyond standard model fields.

hep-th↗
arXiv2023

A geometrical approach to nontrivial topology via exotic spinors

Exotic spinors arise in non-simply connected base manifolds due to the nonequivalent spinor structure. The dynamics of exotic spinors are endowed with an additional differential factor. In this work, we merge the exotic spinor scenario with Cartan's spinor viewpoint, according to which a given spacetime point is understood as a kind of composition of spinor entries. As a result, we arrive at a geometrical setup in which the Minkowski metric is perturbed by elements reflecting the nontrivial topology. Such corrections shall be felt by any physical system studied with the resulting bilinear form. Within the flat spacetime context, we investigate quasinormal modes arising from the interference of nontrivial topology in the scalar field dispersion relation.

math-ph↗
arXiv2023

Quantum Hairy Black Hole Formation and Horizon Quantum Mechanics

After introducing the gravitational decoupling method and the hairy black hole recently derived from it, we investigate the formation of quantum hairy black holes by applying the horizon quantum mechanics formalism. It enables us to determine how external fields, characterized by hairy parameters, affect the probability of spherically symmetric black hole formation and the generalized uncertainty principle.

gr-qc↗
arXiv2022

Spinorial discrete symmetries and adjoint structures

Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify which combination of discrete symmetries may compose a physical and mathematical well-posed spinorial dual. In this scenario, we relate the Lounesto classification with several other spinor classification possibilities, attempting to connect classes and physical constraints. Several possibilities are investigated.

hep-th↗