Jacobi's Action and the Density of States

Details Jacobi's Action and the Density of States Jacobi's Action and the Density of States

1993-01-18

arxiv.org/abs/gr-qc/9301018v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, plain tex. (This replaces the previous version which consisted of less than half of the manuscript.)

Scientific paper

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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