gamma matrices

Quaternion quantum field theory is introduced. The goal is for every equation that plays a role in quantum field theory gets rewritten using real-valued quaternions. Like the correspondence principle before it, the method is simple and systematic: keep 4-vectors together, drop factors of i, keep the constants, but make the expression dimensionless. The differences between classical, relativistic and quantum mechanics equations are based on their constants and form. The uncertainty principles for position/momentum, and energy/time appear in the same expression, a result of the product rule of calculus. The method will shun the most famous equation in physics, , because momentum is omitted. The square of energy-momentum will be used in its place. Substitution in that equation leads directly to the Klein-Gordon equation.

The path to the Dirac equation is more complicated. One needs to know that the 16 gamma matrices can be represented by quaternion triple products. Pre- and post-multiply a quaternion by each combination of the four basis vectors accomplishes the feat. Particular sets of quaternion gamma operators and choices of inertial reference frames can lead to wave functions whose scalar is either positive or negative definite.

A way to visualize quantum field theory using analytical animations is begun. The simplest animation is for an inertial observer. The same number gets added iteratively. The classical view is what one would expect: a ball moving in a straight line at a steady pace. The quantum view show the ball following the same path on average, but the next step cannot be known. Applying the quaternion gamma matrices to inertial path creates 16 possible histories. There is a huge amount of work ahead for the visualization project, but it will look interesting and can be shared with a far greater audience than quaternion quantum field theory equations ever will.