The quaternionic equation of motion of an elementary particle is in fact a continuity equation in which another quaternionic flavor ψʸ of the transporting field ψˣ is coupled with that transporting field via a source term. The coupling factor acts as the mass of the corresponding particle.

This fact comes into the foreground when the Dirac equation is converted from its spinor based form to the much cleaner quaternionic form. After stripping away the matrices and reducing the spinors to a single element, the quaternionic Dirac equation for a free particle runs:

∇ψ = m ψ*

or

∇*ψ* = m ψ

A derived equation is

∇(ψ ψ) = m (ψ ψ*) = 2 m|ψ|²

Another derived equation is

∇(ψ ψ*) = 2 m Re(ψ ψ)

With

∫˯ (ψ ψ*) dV=1

follows

∫˯∇(ψ ψ) dV =2m

m is acoupling factor. It couples two flavors ψ and ψ* of the quaternionic field ψ

Four flavors of field ψ exist; ψ, ψ’, ψ” and ψ*.

The difference switches the sign of 0, 1, 2, resp. 3 imaginary base vectors.

The general form of the equation of motion fo relementary particles is:

∇ψˣ = m ψʸ

This leads to 16 equations. The four equations in which ψˣ equals ψʸ correspond to a zero coupling factor m. Just reversing the field flavors does not work. With the conjugate the nabla must be conjugated as well. The resulting equations correspond to as many categories of elementary particle types that have non-zero coupling factors. Each category contains three sets of coupling factors.

The coupling factor follows from:

∫˯∇( ψˣ ψʸ*)dV = 2m ∫˯ ( ψʸ ψʸ*) dV

This equation also shows that m is a property of the combination ψˣ,ψʸ , which defines the particle. Thus, no Higgs is required in order to give elementary particles their mass.

See details at: http://www.crypts-of-physics.eu/Quaternionic_continuity_equation_for_charges.pdf