Quantum theory of interacting bosons

Eugene P. Gross

S. T. Beliaev

It is shown that the techniques of quantum field theory can be applied to a system of many bosons. The Dyson equation for the one-particle Green’s function is derived. Properties of the condensed phase in a system of interacting bosons are investigated.

Olle Heinonen, M. D. Johnson

Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question as to whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson system in a uniform external field such that there is one flux quantum per particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at half-filling to a boson system at integer filling fails. \textcopyright{} 1996 The American Physical Society.

Peter A. Ring, Y. K. Gambhir, S. Iwasaki +1 more

Shang-Shun Zhang, Zachary M. Raines, Andrey V. Chubukov

The applicability of Eliashberg theory, for fermions interacting with fluctuations of a soft collective boson near a quantum-critical point (QCP) in two dimensions, remains a subject of debate. The velocity of the soft boson is comparable to the Fermi velocity. Hence, Migdal's justification of Eliashberg theory is formally not applicable. The authors argue here that some elements of Migdal's reasoning remain valid because the collective boson is overdamped, yet vertex corrections to Eliashberg theory are $O$(1). At the same time, they show that these corrections are numerically small, at least near an Ising-nematic QCP.

Peter A. Ring, Y. K. Gambhir, S. Iwasaki +1 more