Classical Limits and Critical Properties

  • Robert Gilmore
Part of the Progress in Physics book series (PMP, volume 11)


The classical limit is constructed for systems whose dynamical group is a compact Lie group. The static, thermodynamic, and dynamic properties of such model systems are studied by estimating the ground state energy per particle, the free energy per particle, and the dynamical orbits. These estimates are made by applying a variational principle to the expectation value of the hamiltonian, the free energy, and the lagrangian Operators in the coherent State representation. The expectation values are easily computed in the classical limit. The critical behavior is studied by investigating the behavior of the minima as a function of the parameters which appear in these operators. Relationships among these critical properties (“crossover theorems”) are exhibited. Examples are used to illustrate the concepts which are introduced.


Coherent State Ground State Energy Order Phase Transition Classical Limit Cartan Subalgebra 
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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Robert Gilmore
    • 1
  1. 1.Dept. of Physics and Atmospheric ScienceDrexel UniversityPhiladelphiaUSA

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