LAUSR

Geometric algebra (GA) offers an intriguing approach to understanding the fields of the standard model (SM) of elementary particle physics. This paper examines a geometric view of electron and neutrino fields in the electroweak sector of the SM. These fields are related by the transformations of the $${SU(2)}$$SU(2) Lie group, with generators customarily represented by the $${2\times 2}$$2×2 complex Pauli matrices. In $${\mathcal{G}_3}$$G3, the GA of three-dimensional Euclidean space, the three unit basis vectors may be used to provide a more geometrically oriented representation of $${SU(2)}$$SU(2). In fact, $${\mathcal{G}_3}$$G3 is sometimes referred to as the Pauli algebra. However, a more general representation of the special unitary group $${SU(n)}$$SU(n) in GA is in terms of generators that are compound (non-blade) bivectors in $${\mathcal{G}_{2n}}$$G2n, the GA of $${2n}$$2n-dimensional Euclidean space. Therefore, a natural approach to electroweak theory mathematically is to work with $${SU(2)}$$SU(2) generators as compound bivectors in $${\mathcal{G}_4}$$G4. This approach leads one to consider electroweak fields as multivector fields in $${\mathcal{G}_4}$$G4 that are solutions of the Dirac equation in four spatial dimensions and one time dimension. This paper examines such multivector fields and offers a new point of view on chiral projection of $${\mathcal{G}_3}$$G3 fields. It is shown that $${SU(2)}$$SU(2) representation in $${\mathcal{G}_4}$$G4 leads naturally to the singlet/doublet structure of the chiral electroweak fields.