SOME MULTIDIMENSIONAL INTEGRALS RELATED TO MANY-BODY SYSTEMS WITH THE 1/R2 POTENTIAL
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | IOP PUBLISHING LTD | Published : 1992
An N-dimensional integral evaluated by K Aomoto (1988) is shown to represent the density matrix for an impurity particle in the 1/r2 quantum many-body problem on a line. The value of the N-dimensional integral representing the same density matrix in periodic boundary conditions is conjectured, as too is the value of an N-dimensional integral which represents a two-point correlation function in the system. Also, the partition function of a related classical Hamiltonian is evaluated by formulating a conjecture which asserts that the sum of Jacobians of a certain change of variables in N-dimensions is a constant.