Abstract
The quantization of systems with constraints is of considerable importance in a variety of applications. Let \(\left\{ {pj,{q^j}} \right\},1 \leqslant j \leqslant J \) denote a set of dynamical variables, \( \left\{ {{\lambda ^a}} \right\},1 \leqslant a \leqslant A \leqslant 2J \), a set of Lagrange multipliers, and \(\left\{ {{\phi _a}\left( {p,q} \right)} \right\} \) a set of constraints. Then the dynamics of a constrained system may be summarized in the form of an action principle by means of the classical action (summation implied)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. R. Klauder, Coherent State Quantization of Constraint Systems, IHES/P/96/29, quant-ph/9604033, Annals of Physics (in press); see also quant-ph/9607019 and quant-ph/9607020.
P. A. M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva University, New York, 1964.
L. D. Faddeev, Theor. Math. Phys. 1 (1970), 1.
V. N. Gribov, Nucl. Phys. B139 (1978), 1; I. M. Singer, Commun Math. Phys. 60 (1978), 7; see also J. Govaerts, Hamiltonian Quantisation and Constrained Dynamics, Leuven Notes in Mathematical and Theoretical Physics, Vol. 4, Series B: Theoretical Particle Physics, Leuven University Press, 1991.
M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton University Press, 1992.
S. V. Shabanov, JINR Lecture Notes, Volume 54, Phase Space Structure in Gauge Theories, Dubna (1989) (in Russian); L. V. Prokhorov and S. V. Shabanov, Soy. Phys. Usp. 34 (1991), 108.
V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer, New York, 1978, 75ff and 91f.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Klauder, J.R. (1997). Quantization of Systems with Constraints. In: Gruber, B., Ramek, M. (eds) Symmetries in Science IX. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5921-4_12
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5921-4_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7715-3
Online ISBN: 978-1-4615-5921-4
eBook Packages: Springer Book Archive