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 $2(\pi -8\mathrm{/}3)$ for the particle depletion, and $16(\pi -8\mathrm{/}3)$ for the ground state energy density.