Duality and the Equivalence Principle of Quantum Mechanics

TL;DR

This paper introduces a non-perturbative, metric-free quantum mechanical model that captures S-duality symmetries and links to the equivalence principle, avoiding classical phase space and global quantum numbers.

Contribution

It presents a novel, manifestly non-perturbative quantum mechanics formalism based on topological limit of Berezin's metric quantisation, emphasizing local quantum numbers and reparametrisation invariance.

Findings

Models S-duality as SL(2,R) action on operators

Links quantum mechanics with the equivalence principle

Provides a metric-free, non-perturbative formulation

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.