Perturbation Theory of Many-Boson Systems

Bosonization of Fermionic Many-Body Dynamics

“…2 Unlike the exact bosonization in one-dimensional fermionic systems [41] or in spin systems [10,23,24,43], the bosonization used here is an approximation, however with rigorous control on the error. Our definition of the pair operators has some similarity to the particle-number conserving operators creating an excitation of a Bose-Einstein condensate introduced in [31,37] and used in [5-8, 21, 39, 40, 47].…”

The ground state energy of a Bose gas with Coulomb interaction

“…The second problem is that |φ> does not have a fixed particle number. We solve this by employing a trick which goes back to [8].…”

“…Thus where A t is the Laplacian in the x t variable. The one and two point functions ρ(x), ρ(x, y) for ψ are given by N e(χ)= Σ $\v\ 2 (xi,.-.,Xi-i,x,Xi+i,.-;XN)dx i9 (1)(2)(3)(4)(5)(6)(7)(8)(9) χι> ,χi-ι>χ,χi+ι> ,χj-ι>y>χj+ι> '>χN)dχij. (i.io) t*j…”