Higher-Order Differential Operators on a Lie Group and Quantization

Abstract

This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or representations of Lie groups in those anomalous cases where the Kostant-Kirilov co-adjoint method or the Borel-Weyl-Bott representation algorithm do not succeed.

9 pages, latex, no figures, uses IJMPB.sty (included). New version partially rewritten (title changed!), presented to the II Int. Workshop on Class. and Quant. Integrable Systems, Dubna (Rusia) 1996, and published in Int. J. Mod. Phys. A

Cited by in corpus (8)

• Invariant Measures on Polarized Submanifolds in Group Quantization
• Generalized Conformal Symmetry and Extended Objects from the Free Particle
• Conformal Spinning Quantum Particles in Complex Minkowski Space as Constrained Nonlinear Sigma Models in U(2,2) and Born's Reciprocity
• $SU(2)$-particle sigma model: Momentum-space quantization of a particle on the sphere $S^3$
• A Perturbative Approach to the Relativistic Harmonic Oscillator
• Symmetries of Non-Linear Systems: Group Approach to their Quantization
• Modular Invariance on the Torus and Abelian Chern-Simons Theory
• Thermal Vacuum Radiation in Spontaneously Broken Second-Quantized Theories on Curved Phase Spaces of Constant Curvature