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Classical and Quantum Constraints

  • John R. Klauder
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Many systems involve constraints that generally lead to dynamical motion that is constrained in one way or another. For example, three-dimensional dynamical motion that is constrained to lie on a fixed two-dimensional surface, e.g., motion effectively lying on the surface of the Earth, would constitute constrained motion. Oftentimes, constraints are accompanied by superfluous degrees of freedom, variables whose values are not determined by the equations of motion but whose values must be chosen to fully determine the temporal evolution of the remaining variables. Such variables whose values are left undetermined by the equations of motion are called “gauge” variables; and the somewhat arbitrary choice of such variables to fix the behavior of all the variables is called “choosing a gauge.”

Keywords

Lagrange Multiplier Coherent State Projection Operator Poisson Bracket Reproduce Kernel Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2011

Authors and Affiliations

  1. 1.Department of Physics and Department of MathematicsUniversity of FloridaGainesvilleUSA

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