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Geometric Obstructions on Gravity
These are notes for a short course and some talks gave at Departament of Mathematics and at Departament of Physics of Federal University of Minas Gerais, based on the author's paper arXiv:1808.09249.Expand
On Maximal, Universal and Complete Extensions of Yang-Mills-Type Theories
In this paper we continue the program on the classification of extensions of the Standard Model of Particle Physics started in arXiv:2007.01660. We propose four complementary questions to beExpand
An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories
In this paper we propose an axiomatization for the notion of strong emergence phenomenon between field theories depending on additional parameters, which we call parameterized field theories. WeExpand
Existence of $B^k_{\alpha,\beta}$-Structures on $C^k$-Manifolds.
In this paper we introduce $B_{\alpha,\beta}^{k}$-manifolds as generalizations of the notions of smooth manifolds with $G$-structure or with $k$-bounded geometry. These are $C^{k}$-manifolds whoseExpand
Graph Reconstruction, Functorial Feynman Rules and Superposition Principles
In this article functorial Feynman rules are introduced as large generalizations of physicists Feynman rules, in the sense that they can be applied to arbitrary classes of hypergraphs, possiblyExpand
Geometric Regularity Results on $B_{\alpha,\beta}^{k}$-Manifolds, I: Affine Connections
In this paper we consider the existence problem of affine connections on $C^{k}$-manifolds $M$ whose coefficients are as regular as one needs. We show that if $M$ admits a suitable subatlas, meaningExpand