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Jacobi's Action and the Density of States

J. David Brown·James W. York
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Abstract

The authors have introduced recently a ``microcanonical functional integral" which yields directly the density of states as a function of energy. The phase of the functional integral is Jacobi's action, the extrema of which are classical solutions at a given energy. This approach is general but is especially well suited to gravitating systems because for them the total energy can be fixed simply as a boundary condition on the gravitational field. In this paper, however, we ignore gravity and illustrate the use of Jacobi's action by computing the density of states for a nonrelativistic harmonic oscillator. (Festschrift for Dieter Brill)

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J. David Brown, James W. York. 1993-01-19. Jacobi's Action and the Density of States. https://arxiv.org/abs/gr-qc/9301018

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