Ground State Pressure and Energy Density of a Homogeneous Bose Gas in Two Dimensions

We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state pressure and the ground state energy density to second order in the quantum loop expansion. The renormalization group is used to sum up leading and subleading logarithms from all orders in perturbation theory. In the dilute limit, the renormalization group improved pressure and energy density are essentially expansions in powers of the T-matrix.Comment: 1 figure, revte

Theory of the Weakly Interacting Bose Gas

We review recent advances in the theory of the three-dimensional dilute homogeneous Bose gas at zero and finite temperature. Effective field theory methods are used to formulate a systematic perturbative framework that can be used to calculate the properties of the system at T=0. The perturbative expansion of these properties is essentially an expansion in the gas parameter $\sqrt{na^3}$, where $a$ is the s-wave scattering length and $n$ is the number density. In particular, the leading quantum corrections to the ground state energy density, the condensate depletion, and long-wavelength collective excitations are rederived in and efficient and economical manner. We also discuss nonuniversal effects. These effects are higher-order corrections that depend on properties of the interatomic potential other than the scattering length, such as the effective range. We critically examine various approaches to the dilute Bose gas in equilibrium at finite temperature. These include the Bogoliubov approximation, the Popov approximation, the Hartree-Fock-Bogoliubov approximation, the $\Phi$-derivable approach, optimized perturbation theory, and renormalization group techniques. Finally, we review recent calculations of the critical temperature of the dilute Bose gas, which include 1/N-techniques, lattice simulations, self-consistent calculations, and variational perturbation theory.Comment: 44 pages, 20 Postscript figures. Revised version. Expanded by 7 pages and 4 figs. Updated section on T_c and updated list of references. Discussion on atomic potentials and effective field theory added. Revised version accepted for publication in Review of Modern physic