Complex Projection of Quasianti-Hermitian Quaternionic Hamiltonian Dynamics

TL;DR

This paper studies a specific class of quaternionic quantum Hamiltonian dynamics, showing how their complex projections form semigroup dynamics, with an example involving a spin-1/2 system under a quaternionic potential.

Contribution

It characterizes quasianti-Hermitian quaternionic Hamiltonian dynamics with complex projections as semigroup dynamics, providing a concrete example with a spin-1/2 system.

Findings

Complex projections form one-parameter semigroup dynamics.

Example with spin-1/2 system under quaternionic potential.

Characterization of a subclass of quaternionic Hamiltonian dynamics.

Abstract

We characterize the subclass of quasianti-Hermitian quaternionic Hamiltonian dynamics such that their complex projections are one-parameter semigroup dynamics in the space of complex quasi-Hermitian density matrices. As an example, the complex projection of a spin-1/2 system in a constant quasianti-Hermitian quaternionic potential is considered.