The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors

We propose a cohomological modelling schema of quantum state spaces and their connectivity structures in relation to the formulation of global geometric phase phenomena. In the course of this schema, we introduce the notion of Hermitian differential line sheaves or unitary rays and classify their ga...

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Main Author: Elias Zafiris
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2015/124393
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author Elias Zafiris
author_facet Elias Zafiris
author_sort Elias Zafiris
collection DOAJ
description We propose a cohomological modelling schema of quantum state spaces and their connectivity structures in relation to the formulation of global geometric phase phenomena. In the course of this schema, we introduce the notion of Hermitian differential line sheaves or unitary rays and classify their gauge equivalence classes in terms of a global differential invariant given by the de Rham cohomology class of the curvature. Furthermore, we formulate and interpret physically the curvature recognition integrality theorem for unitary rays. Using this recognition theorem, we define the notion of a quantum spectral beam and show that it has an affine space structure with structure group given by the characters of the fundamental group.
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spelling doaj-art-8c1b1e3fbb3a469b8f15dbd30aaf41552025-02-03T06:45:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/124393124393The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase FactorsElias Zafiris0Department of Mathematics, University of Athens, Panepistimioupolis, 15784 Athens, GreeceWe propose a cohomological modelling schema of quantum state spaces and their connectivity structures in relation to the formulation of global geometric phase phenomena. In the course of this schema, we introduce the notion of Hermitian differential line sheaves or unitary rays and classify their gauge equivalence classes in terms of a global differential invariant given by the de Rham cohomology class of the curvature. Furthermore, we formulate and interpret physically the curvature recognition integrality theorem for unitary rays. Using this recognition theorem, we define the notion of a quantum spectral beam and show that it has an affine space structure with structure group given by the characters of the fundamental group.http://dx.doi.org/10.1155/2015/124393
spellingShingle Elias Zafiris
The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors
Advances in Mathematical Physics
title The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors
title_full The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors
title_fullStr The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors
title_full_unstemmed The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors
title_short The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors
title_sort global symmetry group of quantum spectral beams and geometric phase factors
url http://dx.doi.org/10.1155/2015/124393
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AT eliaszafiris globalsymmetrygroupofquantumspectralbeamsandgeometricphasefactors