Quantization on a Lie group: Higher-order Polarizations
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Contents
* Introduction
-- Why $S^1$-extended phase space?
-- Why central extensions of classical symmetries?
* Central extension \Gt of a group $G$
-- Group cohomology
-- Cohomology and contractions: Pseudo-cohomology
-- Principal bundle with connection $(\Gtm,Θ)$
* Group Approach to Quantization
-- $U(1)$-quantization
-- Non-horizontal polarizations
* Simple examples
-- The abelian group $R^{k}$
-- The semisimple group $SU(2)$
* Algebraic anomalies
-- Higher-order polarizations
-- The Schrödinger group and Quantum Optics
-- The Virasoro group and String Theory
52 pages, latex, no figures. Contribution to "Symmetries in Science X", held in Bregenz (Austria), 13-18 July 1997. To appear in the proceedings
52 pages, latex, no figures. Contribution to "Symmetries in Science X", held in Bregenz (Austria), 13-18 July 1997. To appear in the proceedings