Abstract
We make a comparison between two schemes for quantization of dynamical systems with non-trivial phase space—the geometric quantization based on co-adjoint group orbits and second class constraints method. It is shown that the Hilbert space of a system with second class constraints always has, contrary to the geometric quantization, infinite dimension.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kirilov, A.A.: Elements of the Theory of Representations. Springer, Berlin/Heidelberg/ New York 1976)
Dirac, P.A.M.: Lectures on Quantum Mechanics. Yeshiva University/Academic, New York (1967)
Alekseev, A., Faddeev, L., Shatashvili, S.: J. Geom. Phys. 5, 391–406 (1988)
Wiegman, P.: Nucl. Phys. B323, 311–329 (1989)
Hitchin, N.: Commun. Math. Phys. 131(2), 347–380 (1990)
Gukov, S., Witten, E.: Adv. Theor. Math. Phys. 13, 1–73 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Japan
About this paper
Cite this paper
Stoilov, M. (2014). Quantization on Co-adjoint Group Orbits and Second Class Constraints. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_43
Download citation
DOI: https://doi.org/10.1007/978-4-431-55285-7_43
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55284-0
Online ISBN: 978-4-431-55285-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)