Broken gauge symmetry in a Bose gas with constant particle number

The existence of broken gauge symmetries in Bose-Einstein condensates is still controversially discussed in science, since it would not conserve the total number of particles. Here, it is shown for the first time that non-random condensate and non-condensate phase distributions may arise from local particle number breaking in a Bose gas with constant particle number, while the global U(1)-gauge symmetry of the system is preserved due to particle number conservation.