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
- David Lukas Müller (ORCID: https://orcid.org/0009-0005-7471-0886)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-08-21
- DOI
- https://doi.org/10.5281/zenodo.22047870
- Primary Topic
- Particle physics theoretical and experimental studies
- Type
- preprint