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On the geometric quantization of symplectic Lie group actions

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Date Issued:
1995
Summary:
A general method for the geometric quantization of connected and simply connected symplectic manifolds and the lifting of symplectic Lie group actions is developed. In particular, a geometric construction of multipliers for a Lie group based on the action of the group on a potential of the symplectic form on the manifold is given. These methods are then employed to quantize the 'massive' symplectic homogeneous spaces of the Galilei group and the group action, thereby emphazising the affine structure of the group and deriving a novel form of phase space representations. In the case of nonzero spin we quantize the action of the covering group of the Galilei group. We derive the spin bundles needed from frame bundles over spheres equipped with their natural Levi Civita connection. Furthermore we give a new geometric description of the 'massless' symplectic homogeneous spaces (the coadjoint orbits) of the Galilei group including a description of the group actions and the symplectic forms. We then describe their geometric quantization as well as the lifting of the group action.
Title: On the geometric quantization of symplectic Lie group actions.
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Name(s): Fischer, Bernd Rudolf
Florida Atlantic University, Degree Grantor
Schroeck, Franklin E., Thesis Advisor
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1995
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 114 p.
Language(s): English
Summary: A general method for the geometric quantization of connected and simply connected symplectic manifolds and the lifting of symplectic Lie group actions is developed. In particular, a geometric construction of multipliers for a Lie group based on the action of the group on a potential of the symplectic form on the manifold is given. These methods are then employed to quantize the 'massive' symplectic homogeneous spaces of the Galilei group and the group action, thereby emphazising the affine structure of the group and deriving a novel form of phase space representations. In the case of nonzero spin we quantize the action of the covering group of the Galilei group. We derive the spin bundles needed from frame bundles over spheres equipped with their natural Levi Civita connection. Furthermore we give a new geometric description of the 'massless' symplectic homogeneous spaces (the coadjoint orbits) of the Galilei group including a description of the group actions and the symplectic forms. We then describe their geometric quantization as well as the lifting of the group action.
Identifier: 12413 (digitool), FADT12413 (IID), fau:9310 (fedora)
Note(s): Thesis (Ph.D.)--Florida Atlantic University, 1995.
Subject(s): Symplectic manifolds
Group schemes (Mathematics)
Lie groups
Geometry, Differential
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fcla/dt/12413
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.