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Duality and the Equivalence Principle of Quantum Mechanics

J. M. Isidro
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Abstract

Following a suggestion by Vafa, we present a quantum-mechanical model for S-duality symmetries observed in the quantum theories of fields, strings and branes. Our formalism may be understood as the topological limit of Berezin's metric quantisation of the upper half-plane H, in that the metric dependence has been removed. Being metric-free, our prescription makes no use of global quantum numbers. Quantum numbers arise only locally, after the choice of a local vacuum to expand around. Our approach may be regarded as a manifestly non perturbative formulation of quantum mechanics, in that we take no classical phase space and no Poisson brackets as a starting point. The reparametrisation invariance of H under SL(2,R) induces a natural SL(2,R) action on the quantum mechanical operators that implements S-duality. We also link our approach with the equivalence principle of quantum mechanics recently formulated by Faraggi and Matone.

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J. M. Isidro. 2000-10-09. Duality and the Equivalence Principle of Quantum Mechanics. https://doi.org/10.1142/s0217751x01005353

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