Quasiparticle Transformations

Paul Mandel

A. M. Navon, A. Bose

A theoretical study of single-particle transformations, quasiparticle transformations, Slater determinants, and quasiparticle vacuum states is made for a given finite number of single-fermion states. The usual unitary single-particle or quasiparticle transformations are generalized. The new transformations are the most general transformations which transform Slater determinants into Slater determinants or quasiparticle vacuum states into quasiparticle vacuum states, and they contain as particular cases Thouless's nonunitary transformation. It is shown that several Brillouin theorems used in Hartree-Fock and Hartree-Bogolubov variation theories follow from the form of the continuous variations which can be performed in the space of Slater determinants and in the space of quasiparticle vacuum states.

Orlando Luongo

Franz Mohling

In the first paper of this series, the master-graph formulation of the Lee-Yang quantum statistical theory for a degenerate Bose system was derived. In the present paper, this entire theory is transformed from a free-particle description to a quasiparticle description by means of a $\ensuremath{\Lambda}$ transformation. This transformation leaves the master-graph formulation of the theory essentially unchanged, while at the same time introducing the quasiparticle energy-momentum relation and the quasiparticle interaction function into the theory. The transformation is motivated by a study of the very low-temperature behavior of the fundamental integral equation of the theory. An interesting feature of the transformed theory is that it contains two quasiparticle energy-momentum relations, ${\ensuremath{\epsilon}}_{+}(k)$ and ${\ensuremath{\epsilon}}_{\ensuremath{-}}(k)$. The understanding of this result is not achieved in this paper, although the possibility of a double quasiparticle spectrum has previously been suggested by Lieb.

A. M. Navon

New criteria characterizing Slater determinants and quasiparticle vacuum states are obtained. These criteria are expressed as quadratic homogeneous equations in the coefficients of the development of the trial wavefunction in a basis of Slater determinants. A redefinition of quasiparticle vacuum states permits the introduction of quasiparticle transformations which are more general than the generalized Bogoliubov transformations.