Proceedings of the International Conference on Geometry, Integrability and Quantization

Lectures on Geometric Quantization

Jędrzej Śniatycki

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Abstract

These lectures notes are meant as an introduction to geometric quantization. In Section 1, I begin with presentation of the historical background of quantum mechanics. I continue with discoveries in the theory of representations of Lie groups, which lead to emergence of geometric quantization as a part of pure mathematics. This presentation is very subjective, flavored by my own understanding of the role of geometric quantization in quantum mechanics and representation theory. Section 2 is devoted to a review of geometry of Hamiltonian systems. Geometric quantization is discussed in the next two sections: prequantization in Section 3 and polarization in Section 4. In particular, I discuss geometric quantization with respect to polarizations given by Kähler structure, cotangent bundle projection and completely integrable system. More advanced topics, like metaplectic structure, pairing of polarizations, and commutation of quantization and reduction, are not included.

Article information

Source
Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Guowu Meng and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2016), 95-129

Dates
First available in Project Euclid: 15 December 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1450194153

Digital Object Identifier
doi:10.7546/giq-17-2016-95-129

Mathematical Reviews number (MathSciNet)
MR3445426

Zentralblatt MATH identifier
1345.53001

Citation

Śniatycki, Jędrzej. Lectures on Geometric Quantization. Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, 95--129, Avangard Prima, Sofia, Bulgaria, 2016. doi:10.7546/giq-17-2016-95-129. https://projecteuclid.org/euclid.pgiq/1450194153


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