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Bargmann invariants, null phase curves, and a theory of the geometric phase

Mukunda, N and Arvind, * and Ercolessi, E and Marmo, G and Morandi, G and Simon, R (2003) Bargmann invariants, null phase curves, and a theory of the geometric phase. In: Physical Review A (Atomic, Molecular, and Optical Physics), 67 (4). pp. 42114-1.

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Abstract

We present a theory of the geometric phase based logically on the Bargmann invariant of quantum mechanics, and null phase curves in ray space, as the fundamental ingredients. Null phase curves are themselves defined entirely in terms of the (third order) Bargmann invariant, and it is shown that these are the curves natural to geometric phase theory, rather than geodesics used in earlier treatments. The natural symplectic structure in ray space is seen to play a crucial role in the definition of the geometric phase. Logical consistency of the formulation is explicitly shown, and the principal properties of geometric phases are deduced as systematic consequences.

Item Type: Journal Article
Additional Information: The DOI is currently only displayed. Copyright for this article belongs to American Physical Society (APS)
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Date Deposited: 07 Jun 2004
Last Modified: 19 Sep 2010 04:12
URI: http://eprints.iisc.ernet.in/id/eprint/292

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