Identity by Symmetry Breaking

Abstract

We argue that bounded physical entities — stable particles, cosmological relics, and broken-symmetry vacuum states — are constituted by the joint operation of three structural components. A curvature, geometric or in field space, defines the potential well in which the entity can be localized. A symmetry breaking distinguishes the bound state from a previously degenerate manifold and is constitutive rather than triggering: the entity does not pre-exist the breaking but comes into being at the breaking event, with its identifying labels — mass, charge, coupling pattern, oscillation frequency — selected by that event. A scalar (or scalar-like) field supplies the entity's functional content. We develop this structural reading through three case studies — the photon as the U(1)_em-protected outcome of electroweak symmetry breaking, the QCD axion as a coherent oscillating dark matter candidate produced by stacked Peccei–Quinn and QCD breakings, and the curvature-induced misalignment scenario for non-thermal cold dark matter — and we identify, in each case, the same triadic pattern with different physical fillings. The structural reading produces a falsifiable prediction that generalizes across all three cases: each identity-creation event leaves three classes of observables — features encoded in parameter relations of the symmetric phase, relations set by the breaking itself, and topological features of the post-event configuration — that are determined by three different theoretical structures and are predicted to be functionally independent. We name this three-class observational structure the constitutive fingerprint of an identity-creation event. We identify the specific constitutive fingerprints expected in each case: the Weinberg angle, the ρ parameter, and topological triviality for electroweak symmetry breaking; the isocurvature amplitude, the m_a–f_a relation, and the domain wall problem for the QCD axion; the suppressed isocurvature spectrum, the H_I-independence of relic abundance, and the absence of domain walls for the curvature-induced scenario. The structural reading is observational rather than predictive of new physics, but the constitutive-fingerprint prediction recurs across mechanically distinct cases — and the recurrence is its principal empirical content.

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