Quantization of Systems with Constraints

John R. Klauder
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John R. Klauder: University of Florida, Departments of Physics and Mathematics

A chapter in Symmetries in Science IX, 1997, pp 167-178 from Springer

Abstract: 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) 1 $$I = \int {\left[ {pj{{\dot q}^j} - H\left( {p,q} \right) - {\lambda ^a}{\phi _a}\left( {p,q} \right)} \right]} dt. $$

Keywords: Hilbert Space; Lagrange Multiplier; Coherent State; Classical Action; Reproduce Kernel Hilbert Space (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-5921-4_12

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DOI: 10.1007/978-1-4615-5921-4_12

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