Quantum Entropy for the Fuzzy Sphere and its Monopoles

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.

arXiv comment21 pages, typos corrected

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Cited by in corpus (6)

• Magnetic Monopoles in (Noncommutative) Quantum Mechanics
• Monopoles, Dirac operator and index theory for fuzzy $SU(3)/(U(1)\times U(1))$
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• Black Hole and Fuzzy Objects in BFSS Matrix Model
• Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions
• Emergent Gauge Symmetries and Quantum Operations