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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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| 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. |
| format | Article |
| id | doaj-art-8c1b1e3fbb3a469b8f15dbd30aaf4155 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| 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 |
| work_keys_str_mv | AT eliaszafiris theglobalsymmetrygroupofquantumspectralbeamsandgeometricphasefactors AT eliaszafiris globalsymmetrygroupofquantumspectralbeamsandgeometricphasefactors |