3 research outputs found
Infrared Behavior of Interacting Bosons at Zero Temperature
We exploit the symmetries associated with the stability of the superfluid
phase to solve the long-standing problem of interacting bosons in the presence
of a condensate at zero temperature. Implementation of these symmetries poses
strong conditions on the renormalizations that heal the singularities of
perturbation theory. The renormalized theory gives: For d>3 the Bogoliubov
quasiparticles as an exact result; for 1<d<=3 a nontrivial solution with the
exact exponent for the singular longitudinal correlation function, with phonons
again as low-lying excitations.Comment: Minor Changes. 4 pages, RevTeX, no figures, uses multicol.sty e-mail:
[email protected]
Renormalization Group Approach to the Infrared Behavior of a Zero-Temperature Bose System
We exploit the renormalization-group approach to establish the {\em exact}
infrared behavior of an interacting Bose system at zero temperature. The
local-gauge symmetry in the broken-symmetry phase is implemented through the
associated Ward identities, which reduce the number of independent running
couplings to a single one. For this coupling the -expansion can be
controlled to all orders in (). For spatial dimensions the Bogoliubov fixed point is unstable towards a different fixed point
characterized by the divergence of the longitudinal correlation function. The
Bogoliubov linear spectrum, however, is found to be independent from the
critical behavior of this correlation function, being exactly constrained by
Ward identities. The new fixed point properly gives a finite value of the
coupling among transverse fluctuations, but due to virtual intermediate
longitudinal fluctuations the effective coupling affecting the transverse
correlation function flows to zero. As a result, no transverse anomalous
dimension is present. This treatment allows us to recover known results for the
quantum Bose gas in the context of a unifying framework and also to reveal the
non-trivial skeleton structure of its perturbation theory.Comment: 21 page