The quantum mechanics of affine variables

✍ Scribed by José M. Isidro

• Book ID: 104343063
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 72 KB
• Volume: 41
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(01)00060-2

✦ Synopsis

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 of Berezin's method 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 resulting quantum mechanics turns out to be that of the affine variables of quantum gravity.