Derivation of the Principle of Compensation of Dangerous Diagrams

Abstract

The principle of compensation of dangerous diagrams (PCDD) postulated by Bogoliubov to determine the coefficients in the canonical transformation to quasi‐particles in superconducting systems is derived from four different criteria (1) the expected number of quasi‐particles in the true ground state is a minimum, (2) the one‐particle density matrix and the two‐particle amplitude determined from the BCS ground state are equated to the true ones, (3) the expectation value of an arbitrary operator is simplified by diagonalizing its quadratic part, and (4) the starting point for the dressing of the quasi‐particle is chosen in the most convenient way. The condition obtained for the PCDD is then expressed in terms of quasi‐particle Green's functions. The ladder diagrams are eliminated by examining an integral equation for the Green's function describing the creation of two quasi‐particles from the vacuum. Finally, the condition obtained here for the PCDD is compared with the condition obtained previously.