Symplectic Induction, Unitary Induction and BRST Theory (Summary)

G. M. Tuynman
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G. M. Tuynman: Université de Lille I, UFR de Mathématiques

A chapter in Quantization, Coherent States, and Complex Structures, 1995, pp 119-119 from Springer

Abstract: Abstract The data needed for a unitary representation of a Lie group G are a Hilbert space H (finite or infinite dimensional) and a (linear) action of G on H. This action should preserve the inner product in H. In the same spirit one can define a symplectic and a hamiltonian representation of G. The data needed are a symplectic manifold (M, ω) and an action of G on M. For a symplectic representation this action should preserve ω; for a hamiltonian representation it should also posses an equivariant moment map (which takes values in the dual Lie algebra of G). In these terms the procedure of geometric quantization can be described as a procedure to transform a hamiltonian representation of G into a unitary representation.

Keywords: Coherent State; Unitary Representation; Symplectic Manifold; Closed Subgroup; Geometric Quantization (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1060-8_13

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DOI: 10.1007/978-1-4899-1060-8_13

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