Two Kinds of Anti

The word "anti" carries two meanings that ordinary usage merges. "Antiparticle" names a relation: which object is the dual partner of which. "Antimatter" names a pole: which half of the theory an object belongs to. The second is a choice, and duality does not make it. We show that in the Standard Model the choice has a small and completely enumerable structure. On the channel labels of one left-handed doublet, the involution δ induced by the dual functor and the weak partner transfer τ generate a Klein four-group acting simply transitively, and every dual-odd assignment of poles is a signed character of that group. Exactly two remain: the conventional assignment K, which is even under τ and therefore carries no information about the weak factor beyond an independently chosen particle half, and the diagonal M, which is odd under both generators and realizes L_K = A ⊕ B ↦ L_M = A ⊕ Bᵛ as a partial dualization of the down-type sector. Color multiplicity, common weak-root homogeneity and degree zero on the electroweak 't Hooft tensor align the four doublet copies of one generation and select [±M] uniquely. The Higgs frames a representative and transports it to the right-handed channels, giving M = (B−L) − 2Q after symmetry breaking. On local gauge singlets the grading restricts exactly to B−L, which fixes the reach of the construction. The charge direction R = (B−L) − 2Y is itself known; what is offered here is its selection as a noncentral channel lift, together with two readings of that selection: the degree of the 't Hooft vertex is four per generation for K = 3B + L, which is fermion number and the charge the electroweak anomaly violates, and zero for M; and in left–right and Spin(10) embeddings M = −2(T_3L + T_3R) is symmetric in the two isospins, while K admits no Cartan-plus-constant realization even on the 10 of SU(5).

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-21
DOI
https://doi.org/10.5281/zenodo.22047871
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

Two Kinds of Anti

David Lukas Müller
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

Two Kinds of Anti

David Lukas Müller
preprint en

Abstract

The word "anti" carries two meanings that ordinary usage merges. "Antiparticle" names a relation: which object is the dual partner of which. "Antimatter" names a pole: which half of the theory an object belongs to. The second is a choice, and duality does not make it. We show that in the Standard Model the choice has a small and completely enumerable structure. On the channel labels of one left-handed doublet, the involution δ induced by the dual functor and the weak partner transfer τ generate a Klein four-group acting simply transitively, and every dual-odd assignment of poles is a signed character of that group. Exactly two remain: the conventional assignment K, which is even under τ and therefore carries no information about the weak factor beyond an independently chosen particle half, and the diagonal M, which is odd under both generators and realizes L_K = A ⊕ B ↦ L_M = A ⊕ Bᵛ as a partial dualization of the down-type sector. Color multiplicity, common weak-root homogeneity and degree zero on the electroweak 't Hooft tensor align the four doublet copies of one generation and select [±M] uniquely. The Higgs frames a representative and transports it to the right-handed channels, giving M = (B−L) − 2Q after symmetry breaking. On local gauge singlets the grading restricts exactly to B−L, which fixes the reach of the construction. The charge direction R = (B−L) − 2Y is itself known; what is offered here is its selection as a noncentral channel lift, together with two readings of that selection: the degree of the 't Hooft vertex is four per generation for K = 3B + L, which is fermion number and the charge the electroweak anomaly violates, and zero for M; and in left–right and Spin(10) embeddings M = −2(T_3L + T_3R) is symmetric in the two isospins, while K admits no Cartan-plus-constant realization even on the 10 of SU(5).

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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Two Kinds of Anti — David Lukas Müller · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS