Quantization on a Lie group: Higher-order Polarizations

Details Quantization on a Lie group: Higher-order Polarizations Quantization on a Lie group: Higher-order Polarizations

1997-10-03

arxiv.org/abs/physics/9710002v1

Physics

Mathematical Physics

52 pages, latex, no figures. Contribution to "Symmetries in Science X", held in Bregenz (Austria), 13-18 July 1997. To appear

Scientific paper

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 $(\Gtm,\Theta)$ * 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 Schr\"odinger group and Quantum Optics -- The Virasoro group and String Theory

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