A Dirac Doublet Action with Nonlinear Alignment Interaction

This paper formulates a nonlinear single-doublet matter action in the real spacetime algebra Cl(1,3). The central object is a Clifford-Dirac doublet, represented as the spacetime-split form of a single real multivector field. The doublet embedding contains an intrinsic alignment structure, which separates the field into reinforcing and cancellation channels. The charged-massive single-doublet assignment studied in the paper places the electromagnetic source and the scalar Dirac mass bilinear on the same selected alignment eigenchannel. With the oriented embedding used in the paper, this is the reinforcing channel. The action also includes a local Lorentz-scalar current-current alignment interaction between the two channels. In the regular common-orientation sector, this interaction penalizes simultaneous occupation of both alignment channels and favours the pure alignment eigenstates. In the pure reinforcing limit, the field equations reduce to a charged massive Dirac equation with signed electromagnetic coupling and signed first-order mass-rotation parameter. In the pure cancellation limit, the field equations reduce to a neutral massless equation at exact alignment. When both channels are populated, the same action describes a nonlinear mixed-channel regime in which each channel evolves in a real vector source generated by the current of the other channel. The selected dimensionless electromagnetic charge operator is identified with the alignment-channel projector associated with the charged branch. On the left-projected weak sector, this reproduces a shifted charged/neutral projector structure analogous to the one appearing in the electroweak charge formula. The off-diagonal projected weak generators then carry the dimensionless charge difference between the selected charged and neutral alignment channels. The result is a candidate single-doublet Clifford mechanism for the charged/neutral, massive/massless, and weak charge-transfer structure of one lepton-like doublet. Generation replication, quark-sector assignments, electroweak mixing, the origin of the alignment interaction, mixed-orientation sectors, multi-doublet charge bookkeeping, and full gauge-field dynamics are left for later work.