GEOMETRIC QUANTIZATION

Proceedings of the Winter Research Institute on Geometric Quantization, Banff, Canada, 1981

Edited by: Mark J. Gotay

Preface:

The purpose of the Banff Winter Research Institute was to provide an opportunity for researchers to gather and discuss recent developments in geometric quantization theory and related fields. The Institute was intended to be a "working" conference and its theme was "infomality," enabling participants to freely report their latest ideas, results and speculations in a relaxed setting. The magnificient backdrop of the Canadian Rockies served to enhance this atmosphere. I am sure that all participants will join me in thanking Jedrzej Sniatycki and Joe Wolf for their work in organizing a very stimulating and successful meeting.

Since its inception in the late1960's and early 1970's, the field of geometric quantization has evolved tremendously. It has grown into a powerful tool in group representation theory and has found important applications in many other areas of mathematics. As well, geometric quantization has provided significant insights into both classical and quantum physics. These various advances are reflected in the Proceedings; virtually every facet of geometric quantization is represented and explored in the contributed papers. The next several years should prove to be quite exciting for the development of geometric quantization theory and its applications. Beyond simply summarizing the state of the art, these Proceedings point the way for its future development.

Index:

• List of Participants
• Robert J. Blattner, Ladder Representations of U(k,l), 9 pps.
• Michel Duflo, Mackey's Theory for Algebraic Groups, 13 pps.
• Mark J. Gotay, Cosiotropic Imbeddings, Dirac Brackets and Quantization, 16 pps.
• V. Guillemin and S. Sternberg, The Marsden-Weinstein Theorem and Geometric Quantization, 10 pps.
• Christian Günther, Logic, Dynamics and Symmetry, 13 pps.
• Roger Howe, Dual Pairs and the Classical Equations of Physics, 28 pps.
• James A. Isenberg, Geometric Quantization of Homogeneous Field Theories, 6 pps.
• Witold Kondracki and Jan Rogulski, The Stratification Structure in the Space of Gauge-Equivalent Yang-Mills Connections, 19 pps.
• Jerrold E. Marsden and Alan Weinstein, The Hamiltonian Structure of the Maxwell-Vlasov Equations, 28 pps.
• Stephen M. Paneitz, Existence and Uniqueness of Invariant Quantization of Linear Symplectic Differential Equations, 9 pps.
• J. H. Rawnsley, Non-Positive Polarizations and Half-forms, 9 pps.
• George Rosensteel, Geometric Quantization and Nuclear Structure Physics, 12 pps.
• Wilfried Schmid and Joseph A. Wolf, Singular Unitary Representations and Indefinite Harmonic Theory, 10 pps.
• D. J. Simms, On Deriving Quantum Mechanics by Geometric Quantization, 5 pps.
• Jedrzej Sniatycki, On Geometric Quantization Interpretation in Field Theory, 5 pps.
• J.-M. Souriau, Groupes Differentiels, 39 pps.
• David A. Vogan, Jr., Singular Unitary Representations, 31 pps.
• Alan Weinstein, The Symplectic "Category", 8 pps.
• Nicholas M. J. Woodhouse, Geometric Quantization and the Bogoluibov Transformation, 6 pps.
• Gregg J. Zuckerman, Representations of Lie Groups, 3 pps.
• Gregg J. Zuckerman, Derived Functor Modules, 3 pps.

To obtain articles, contact the individual authors.

Info:

290 pps. 1981 Published as: Geometric Quantization. (Proc. of the Winter Research Institute on Geometric Quantization, Banff, Canada.) (Univ. of Calgary, Calgary), 1981.

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