Octonionic Quantum Mechanics and Complex Geometry
Stefano De Leo, Khaled Abdel-Khalek (Lecce Univ.)
TL;DR
This paper develops a consistent formulation of octonionic quantum mechanics using complex geometry, addressing key issues like hermiticity, momentum operator definition, and norm conservation.
Contribution
It introduces a novel octonionic quantum mechanics framework that resolves hermiticity and momentum operator problems using complex geometric methods.
Findings
Resolved hermiticity problem in OQM
Defined an appropriate momentum operator in OQM
Discussed limitations of completeness relation and norm conservation
Abstract
The use of complex geometry allows us to obtain a consistent formulation of octonionic quantum mechanics (OQM). In our octonionic formulation we solve the hermiticity problem and define an appropriate momentum operator within OQM. The nonextendability of the completeness relation and the norm conservation is also discussed in details.
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