Nonadiabatic Geometric Phase in Quaternionic Hilbert Space
Stephen L. Adler, Jeeva Anandan
TL;DR
This paper extends the concept of nonadiabatic geometric phases to quaternionic Hilbert spaces, covering both Abelian and non-Abelian cases, advancing the theoretical understanding of geometric phases in quaternionic quantum mechanics.
Contribution
It introduces a comprehensive theoretical framework for nonadiabatic geometric phases in quaternionic Hilbert spaces, including Abelian and non-Abelian cases, which was not previously developed.
Findings
Formulation of nonadiabatic geometric phase in quaternionic Hilbert space
Extension of geometric phase concepts to non-Abelian cases in quaternionic setting
Foundational theoretical results for quaternionic quantum mechanics
Abstract
We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.
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