Principle of Compensation of Dangerous Diagrams for Boson Systems. II. Minimum Quasiparticle Number

Abstract

The principle of compensation of dangerous diagrams (PCDD) postulated by Bogoliubov to determine the coefficients in his canonical transformation in boson systems is obtained from four criteria: (1) the number of quasiparticles in the true ground state is a minimum; (2) the ``best'' approximation to the true density matrix and pair amplitude is made; (3) the expectation value of an arbitrary operator is diagonalized up to terms cubic in the quasiparticle operators; (4) the most convenient starting point for dressing the quasiparticles is used. Quasiparticle Green's functions are introduced to obtain a diagrammatic expansion of the PCDD. The reducibility of the diagrams is also discussed.