Single-particle Green functions in exactly solvable models of Bose and Fermi liquids

Abstract

Based on a class of exactly solvable models of interacting bose and fermi liquids, we compute the single-particle propagators of these systems exactly for all wavelengths and energies and in any number of spatial dimensions. The field operators are expressed in terms of bose fields that correspond to displacements of the condensate in the bose case and displacements of the fermi sea in the fermi case. Unlike some of the previous attempts, the present attempt reduces the answer for the spectral function in any dimension in both fermi and bose systems to quadratures. It is shown that when only the lowest order sea-displacement terms are included, the random phase approximation in its many guises is recovered in the fermi case, and Bogoliubov's theory in the bose case. The momentum distribution is evaluated using two different approaches, exact diagonalisation and the equation of motion approach.The novelty being of course, the exact computation of single-particle properties including short wavelength behaviour.

Sea-boson theory of Landau-Fermi liquids, Luttinger liquids and Wigner crystals

“…This rectifies some serious errors of judgement of previous works 1 . In addition, we are able to solve for the one-particle properties of various systems highlighted in the abstract.…”

U(1) Gauge theory as quantum hydrodynamics

“…As pointed out in an earlier work [8] the phase variable may be written as a sum of two terms a position independent term which is the conjugate to the total number and a position dependent term that is related to currents and densitites. Thus, Π(x) = X 0 +Π(x).…”

“…In our next article, we shall see that the density phase variable ansatz (DPVA) for fermions [8] which includes a phase functional that is nonlocal in position space also leads to a Jacobian that is constant. This can be checked using the Mathematica T M software.…”

“…In general however, it does not. Now we would like an expression for the field operator also in terms of C. Using the DPVA [8] in terms of currents and densities we may write,…”

“…Every complex number can be decomposed into a magnitude and a phase. Using the ideas explained in our earlier work [8] ψ…”