Quaternionic quantum mechanics in real Hilbert space
Quantum Physics
2021-01-12 v1 Mathematical Physics
math.MP
Abstract
A formulation of quaternionic quantum mechanics (QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After a brief discussion on unitary operators in this formalism, we conclude that this quantum theory is indeed consistent, and can be a valuable tool in the search for new physics.
Cite
@article{arxiv.1803.11523,
title = {Quaternionic quantum mechanics in real Hilbert space},
author = {Sergio Giardino},
journal= {arXiv preprint arXiv:1803.11523},
year = {2021}
}