QuasiParticle Description of a Degenerate System of Bosons
Abstract
The infrared divergence of the interaction among Bogoliubov's quasiparticles in a degenerate boson system can be avoided by introducing improved quasiparticles. A formula is given which relates the singleparticle operators a_{P} directly to the improved quasiparticle operators b_{P}, which have been defined in terms of collective, variables in a preceding paper. The operators a_{P} are expressed in terms of b_{P} as a series using N^{1/2} as a formal expansion parameter, where N is the number of particles in the system. Terms up to order N^{3/2} are given together with a term of order N^{2} which is necessary for the calculation of the groundstate energy to order N^{2}. The formula makes the reason clear why the operators b_{P} enable us to eliminate the ultraviolet divergence haunting collective theories including the quantum hydrodynamics.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 November 1982
 DOI:
 10.1143/PTP.68.1482
 Bibcode:
 1982PThPh..68.1482H