We exploit the symmetries associated with the stability of the superfluid phase to solve the long-standing problem of interacting bosons in the presence of a condensate at zero temperature. Implementation of these symmetries poses strong conditions on the renormalizations that heal the singularities of perturbation theory. The renormalized theory gives the following: For $d>\mathrm{}3\mathrm{}$ the Bogoliubov quasiparticles as an exact result; for $1<d\le 3$ a nontrivial solution with the exact exponent for the singular longitudinal correlation function, with phonons again as low-lying excitations.

• Received 22 March 1996

DOI:https://doi.org/10.1103/PhysRevLett.78.1612