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The classical limit of quantum partition functions

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Abstract

We extend Lieb's limit theorem [which asserts that SO(3) quantum spins approachS 2 classical spins asL→∞] to general compact Lie groups. We also discuss the classical limit for various continuum systems. To control the compact group case, we discuss coherent states built up from a maximal weight vector in an irreducible representation and we prove that every bounded operator is an integral of projections onto coherent vectors (i.e. every operator has “diagonal form”).

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Authors and Affiliations

  1. Departments of Mathematics and Physics, Princeton University, 08544, Princeton, NJ, USA

    Barry Simon

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  1. Barry Simon
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Communicated by E. Lieb

Supported by USNSF Grant MCS-78-01885

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Simon, B. The classical limit of quantum partition functions. Commun.Math. Phys. 71, 247–276 (1980). https://doi.org/10.1007/BF01197294

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  • DOI: https://doi.org/10.1007/BF01197294

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