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arXiv · 1405.6471

Quantum Entropy for the Fuzzy Sphere and its Monopoles

Nirmalendu Acharyya·Nitin Chandra·Sachindeo Vaidya
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Abstract

Using generalized bosons, we construct the fuzzy sphere $S_F^2$ and monopoles on $S_F^2$ in a reducible representation of $SU(2)$. The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent non-abelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

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Nirmalendu Acharyya, Nitin Chandra, Sachindeo Vaidya. 2014-06-02. Quantum Entropy for the Fuzzy Sphere and its Monopoles. https://doi.org/10.1007/jhep11(2014)078

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