Can the mass of the various particles be calculated from this framework? Presently, the masses of the particles is something that is simply measured in accelerators. But it occurs to me that it might be possible to calculate the mass of the particles, at least in comparison with

electron mass. In my previous post in this thread,

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=440#p11361, I use an iterative procedure to show how the

Weak bosons and

quarks can be constructed from

electrons and

positrons. And then later in this thread,

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=440#p11402, I write out the math of this iterative procedure.

The transition amplitude of a free

electron was given in the form,

.

And for the purposes of this point, this can be simplified to,

,

where the

is some normalization factor, and the

is some exponential function that includes the constant

, the mass of the

electron.

The iterative procedure consists of inserting this exponential function back into the transition amplitude to get,

,

which is an eponential function inside an exponential. The

is for the complex numbers, and the

is for the quaternions, and the

is the mass scale of the

Weak particles. This iteration seems to at least give us the correct number of

Weak bosons, see previous posts. But ultimately these bosons are expressed in terms of the

electron/

positron amplitudes. If we iterate again, we get,

.

This is an exponent inside an exponent inside an exponent, the

is for the octonions, and

is the mass scale of the

quarks. This seems to give us the correct number of first mass generataion

quarks.

Now it seems to me that the mass of a particle is only relevant in interactions between particles and in the calculations of probabilities. So it seems that the particles need to propagate with the usually constructed amplitude to do these calculations, with a leading normalization factor and a complex exponential that oscillates like the amplitude of an

electron/

positron.

So the question is whether it is possible to put these exponentials inside exponential functions into the form of just a complex exponential of maybe just the first squared term. Then the mass term for the heavier particles might be a complicated function of the masses of the lighter particles. However, I don't see how this can be done analytically. But it might be possible to come up with an expansion for exponential functions that are inside others. Then we might have a series expansion that would give us ever more accurate approximations, assuming it converges. But then we would also have quaternions and octonions that have to somehow be reduced to simple complex numbers. I'm not sure of any general procedures for doing that.

Such a process would be simpler, of course, if the iteration process were blind to the mass scale. If the mass scale terms,

and

, were equal to

, the calculations would be easier. Or it might be that we have to iterate the mass scale along with iterating from complex to quaterions to octonions.

I would appreciate any ideas on how to do such calculations. Is there any software package geared for these kinds of hypercomplex calculations?