On the infimum of the energy-momentum spectrum of a homogeneous Bose gas

We consider second quantized homogeneous Bose gas in a large cubic box with periodic boundary conditions, at zero temperature, and in the grand canonical setting (the chemical potential μ is fixed, the number of particles can vary). We investigate upper bounds on the infimum of the energy for a fixed total momentum k given by the expectation value at one-particleexcitations over a squeezed state. We show that the results of the Bogoliubov approach (usually derived heuristically) coincide with the results of the firstiteration of our method (which leads to rigorous upper bounds).