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arXiv · 2306.10771

Oxidation, Reduction and Semi-Classical Limit for Quantum Matrix Geometries

Laura O. Felder·Harold C. Steinacker
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Abstract

Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including noncommutative gauge theory and emergent gravity. Refining the construction in [1], we construct a semi-classical limit through an immersed submanifold of complex projective space based on quasi-coherent states. We observe the phenomenon of oxidation, where the resulting semi-classical space acquires spurious extra dimensions. We propose to remove this artifact by passing to a leaf of a carefully chosen foliation, which allows to extract the geometrical content of the noncommutative spaces. This is demonstrated numerically via multiple examples.

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Laura O. Felder, Harold C. Steinacker. 2023-06-19. Oxidation, Reduction and Semi-Classical Limit for Quantum Matrix Geometries. https://doi.org/10.1016/j.geomphys.2024.105163

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