Ground state energy density of a dilute Bose gas in the canonical transformation

A ground state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order $n a^3$ in the particle depletion and ground state energy density of a dilute Bose gas system, which corresponds to the density fluctuation contribution from the excited states. The coefficient of $n a^3$ term is shown to be $2(\pi - 8/3)$ for the particle depletion, and $16(\pi - 8/3)$ for the ground state energy density.