Gomes, Henrique (2025) Particles before symmetry. [Preprint]

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Abstract

The standard model of particle physics is usually cast in symmetry-first terms. Recently, a geometry-first picture has been proposed, in which the relevant symmetries do not appear explicitly at the ground level of ontology. In this paper I extend this approach to two central mechanisms of the standard model: spontaneous symmetry breaking and the Yukawa coupling, both essential for particles to acquire mass. These reformulations offer alternative explanations cast in purely geometric terms. For example, a particle’s quantum numbers correspond to the internal space it inhabits and to the geometric type of object it is (e.g.\ an $(n,m)$-tensor). I argue that a symmetry-first account in terms of principal and associated bundles admits a genuine geometry-first counterpart only when the group’s representation coincides with the automorphism group of the fibre—a condition that cuts the slack tolerated by the symmetry-first view.In particular, the quantisation of charge arises here as a purely geometric
consequence of the tensorial construction of matter fields from the fundamental
bundles—a mechanism that is both more general and more transparent than the usual
topological account based on the compactness of $U(1)$. More generally, I argue that a symmetry-first account in terms of principal and associated bundles admits a genuine geometry-first counterpart only under certain conditions.

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Item Type:	Preprint
Creators:	Creators Email ORCID Gomes, Henrique gomes.ha@gmail.com 0000-0002-9285-0090
Keywords:	Symmetry, fiber bundles, standard model, particle theory.
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	Dr Henrique Gomes
Date Deposited:	22 Oct 2025 11:08
Last Modified:	22 Oct 2025 11:08
Item ID:	26995
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Fields and Particles Specific Sciences > Physics > Symmetries/Invariances
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/26995

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