On Maximal, Universal and Complete Extensions of Yang-Mills-Type Theories
Résumé
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 be considered when trying to classify any class of extensions of a fixed Yang-Mills-type theory $S^G$: existence problem, obstruction problem, maximality problem and universality problem. We prove that all these problems admits a purely categorical characterization internal to the category of extensions of $S^G$. Using this it is showed that maximality and universality are dense properties, meaning that if they are not satisfied in a class $E(S^G ;Ĝ)$, then they in their "one-point compactification" by a specific trivial extension Ŝ. We prove that, by means of assuming Axiom of Choice, one can get another maximality theorem, now independent of the trivial extension Ŝ. We considered the class of almost coherent extensions, i.e, complete, injective and of pullback-type, and we show that for it the existence and the obstruction problems have a complete solution. Using again the Axiom of Choice, we prove that this class of extensions satisfies the hypothesis of the second maximality theorem.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...