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| The wave equation for the boson is | |
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where 
Expanding the equation as follows |
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For 
and multiplying both sides by 
the following equation is obtained |
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| which can be written as | |
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Comparison with the Dirac Equation gives 
as the Hamiltonian.
It can be shown that the set of matrices Consequently the Hamiltonian Two other Hamiltonians The condition that |
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Thus the number of components of  reduces
to 4.
The rest mass of the fermion is thus dependent on It follows that for each Hamiltonian The Hamiltonians
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are equivalent to the Dirac Gamma Matrices.
now
describe fermions.
can
be obtained in a similar fashion.
leads
to
.
there is different rest mass, which suggests the possibility that there
are indeed 3 generations of fermions.
are
functions of the generalised charge 
where
