Quaternion Series Spin

Abstract

Quantum mechanics today uses a complex-valued Hilbert vector space for its mathematical substructure. Quaternion series quantum mechanics is an effort to replace every complex number with a quaternion. Each quaternion can represent physical quantitie such as events in space-time, 4-potentials, energy-momentum, 4-currents, etc.. A series of quaternions is a vector. One can multiply quaternion series together because the quaternion series are a semigroup with inverses. This may of limited utility given the key roll of unitarity to quantum mechanics.

The intrinsic spin of a particle can be described by a quaternion series with two state dimensions. The spin operator is often characterized as one quaternion. With quaternion series quantum mechanics, spin operators are 2x2 matrices of quaternions, so four simple quaternions in all (zero, plus one, and negative one, normalized is one possible representation). Much effort is devoted to understanding the operators. If one instead examines what a spin operator does to a spin state, there is a simple message: spin operators can mix information found in a spin state in every possible way.