Trace formula for a system of particles with elliptic potential

K.L. Vaninsky

Vol. 189 (1999), No. 1, 159–178

DOI: 10.2140/pjm.1999.189.159

Abstract

We consider classical particles on the line with the Weierstrass ℘ function as potential. This system parameterizes special solutions of the KP equation. We derive the trace formula which relates the Hamiltonian of the particle system to the residues of some Abelian differential (meromorphic one-form) on the spectral curve. Such formula is important for the construction action-angle variables and study invariant Gibbs’ states.

Milestones

Received: 25 September 1997

Revised: 1 May 1998

Published: 1 May 1999