Nonequivalence of N-fixed and $mu$-fixed formalisms adopting a$sub 0$ = a$sub 0$ = N$sub 0$/sup 1/2/ for condensed Bose systems
J.C. Lee · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1975
The idea of replacing the condensate operators by the c number N$sub 0$$sup 1$/$sup 2$ in treating condensed Bose systems is known as Bogoliubov prescription (BP). Once BP is adopted, there are two ways to proceed. The first is the popular method of Hugenholtz and Pines, which we call $mu$-fixed formalism. The second may be found in the well-known works of Foldy and Brueckner on a dense charged boson gas. Unlike the $mu$-fixed formalism, the latter method does not require the introduction of the chemical potential, and thus it is called the N- fixed formalism. We argue that BP is rigorous in the $mu$-fixed formalism but is not in the N-fixed one. BP in the N-fixed one gives correct results for terms of leading orders (Foldy and Brueckner took just these terms) but incorrect results for terms of higher orders. (auth)