In the HyperDiamond Feynman Checkerboard model
the mass parameter m is the amplitude for a particle
to change its spacetime direction. Massless particles
do not change direction, but continue on the same
lightcone path.
In the D4-D6-E6-E7 Lagrangian continuum version
of this physics model, particle masses are calculated in terms
of relative volumes of bounded complex homogeneous domains and
their Shilov boundaries.
The relationship between
the D4-D6-E6-E7 Lagrangian continuum approach
and
the HyperDiamond Feynman Checkerboard discrete approach
is that:
the bounded complex homogeneous domains correspond to
harmonic functions of generalized Laplacians
that determine heat equations, or diffusion equations;
while the amplitude to change directions in the
HyperDiamond Feynman Checkerboard is a diffusion process
in the HyperDiamond spacetime, also corresponding to
a generalized Laplacian.
Details of the D4-D6-E6-E7 Lagrangian continuum approach
can be found on the World Wide Web at URLs
http://xxx.lanl.gov/abs/hep-ph/9501252
Dynamics of this D4 − D5 − E6 model are given by a Lagrangian action
that is the integral over spacetime of a Lagrangian density made up of a
gauge boson curvature term, a spinor fermion term (including through a
Dirac operator interaction with gauge bosons), and a scalar term.
For the discrete HyperDiamond Feynman Checkerboard
approach of this paper, the only free mass parameter
is the mass of the Higgs scalar. All other particle
masses are determined as ratios with respect to the
Higgs scalar and each other.
The Higgs mass is 145.789 GeV in the
HyperDiamond Feynman Checkerboard model,
since the Higgs Scalar field vacuum expectation value v
is set at 252.514 GeV, a figure chosen so
that the mass ratios of the model will give an electron
mass of 0.5110 MeV.
