metrics
A quaternion variation on the metric is explored. The quaternion approach takes into account phase, which could be an improvement. Rotations and boosts work as expect for quaternions. The Einstein summation convention will not be used in this body of work, nor with covariant or contravariant vectors because there are no indices. A variety of conjugates will be used in their place. An open technical issue is how to deal with derivatives in curved quaternion spacetime.
1. The Metric and Its Quaternion Square Root
2. Rotations and Boosts
3. Conjugate Operators
1. The Metric and Its Quaternion Square Root
A spacetime metric tensor takes as inputs 2 4-vectors and returns a Lorentz invariant scalar. An inverse metric is well-defined, but curiously, not a product of two metrics. Write the definition of a metric in a non-standard way:
[tex]g_{\mu \nu }=\left(
\begin{array}{cccc}
g_0g_0 & g_0g_1 & g_0g_2 & g_0g_3 \\
g_1g_0 & g_1g_1 & g_1g_2 & g_1g_3 \\
