SIMILARITY TRANSFORMATIONS AND QUANTUM STATISTICS

The invariance of the partition function to operator similarity transformations is exploited as a tool in quantum statistics. Detailed application is made to a fluid system of interacting bosons where the ground state wave function is real and nodeless. We perform a similarity transformation whose generator is a function only of the coordinates and is in fact the logarithm of the ground state wave function. The non-Hermitian transformed Hamiltonian is governed by the generator rather than by the original potential. The contribution of the ground state to the canonical partition function occurs as a simple factor-the remaining factor describes the excitation gas. It is simple to insure a proper count of the states of the system. This leads to a picture of number constrained excitations and thus to an Einstein condensation even for strongly interacting particles. The spectrum of excitations is only weakly temperature dependent except in the long wavelength limit. © 1969.