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

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  • Elias Zafiris

Abstract

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.

Suggested Citation

  • Elias Zafiris, 2015. "The Global Symmetry Group of Quantum Spectral Beams and Geometric Phase Factors," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:124393
    DOI: 10.1155/2015/124393
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    References listed on IDEAS

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    1. Anastasios Mallios, 2006. "Modern Differential Geometry in Gauge Theories," Springer Books, Springer, number 978-0-8176-4474-1, March.
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    1. Anastasios Mallios & Elias Zafiris, 2011. "The Homological Kähler‐de Rham Differential Mechanism: II. Sheaf‐Theoretic Localization of Quantum Dynamics," Advances in Mathematical Physics, John Wiley & Sons, vol. 2011(1).

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