Coquaternionic quantum dynamics for two-level systems

TL;DR

This paper explores the unique dynamical behaviors of spin-1/2 particles within coquaternionic quantum theory, revealing how different parameter regimes lead to varied unitary evolutions and state space geometries.

Contribution

It introduces a detailed analysis of coquaternionic quantum dynamics for two-level systems, highlighting new types of evolution depending on Hamiltonian parameters.

Findings

Real eigenvalues lead to spherical or hyperbolic state space evolution.

Complex conjugate eigenvalues result in closed orbits despite hyperbolic state space.

Dynamical characteristics depend critically on Hamiltonian parameter values.

Abstract

The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the Hamiltonian. When energy eigenvalues are real, the evolution is either isomorphic to that of a complex Hermitian theory on a spherical state space, or else it remains unitary along an open orbit on a hyperbolic state space. When energy eigenvalues form a complex conjugate pair, the orbit of the time evolution closes again even though the state space is hyperbolic.