260 research outputs found
Collective Variables of Fermions and Bosonization
We first present a general method for extracting collective variables out of
non-relativistic fermions by extending the gauge theory of collective
coordinates to fermionic systems. We then apply the method to a system of
non-interacting flavored fermions confined in a one-dimensional
flavor-independent potential. In the limit of a large number of particles we
obtain a Lagrangian with the Wess-Zumino-Witten term, which is the well-known
Lagrangian describing the non-Abelian bosonization of chiral fermions on a
circle. The result is universal and does not depend on the details of the
confining potential.Comment: 12 pages, plain tex, added new preprint numbe
Annihilation Diagrams in Two-Body Nonleptonic Decays of Charmed Mesons
In the pole-dominance model for the two-body nonleptonic decays of charmed
mesons and , it is shown that the
contributions of the intermediate pseudoscalar and the axial-vector meson poles
cancel each other in the annihilation diagrams in the chiral limit. In the same
limit, the annihilation diagrams for the decays vanish
independently.Comment: 9 pages (+ 3 figures available upon request), UR-1316, ER-40685-766,
IC/93/21
Bulk and edge excitations of a Hall ferromagnet
In this article, we shall focus on the collective dynamics of the fermions in
a quantum Hall droplet. Specifically, we propose to look at the
quantum Hall ferromagnet. In this system, the electron spins are ordered in the
ground state due to the exchange part of the Coulomb interaction and the Pauli
exclusion principle. The low energy excitations are ferromagnetic magnons. In
order to obtain an effective Lagrangian for these magnons, we shall introduce
bosonic collective coordinates in the Hilbert space of many-fermion systems.
These collective coordinates describe a part of the fermionic Hilbert space.
Using this technique, we shall interpret the magnons as bosonic collective
excitations in the Hilbert space of the many-electron Hall system. Furthermore,
by considering a Hall droplet of finite extent, we shall also obtain the
effective Lagrangian governing the spin collective excitations at the edge of
the sample.Comment: 30 pages, plain TeX, no figure
Superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors
We study the quantum phase transition between the superfluid and the Mott
insulator in the one-dimensional (1D) Bose-Hubbard model. Using the
time-evolving block decimation method, we numerically calculate the tunneling
splitting of two macroscopically distinct states with different winding
numbers. From the scaling of the tunneling splitting with respect to the system
size, we determine the critical point of the superfluid to Mott insulator
transition for arbitrary integer filling factors. We find that the critical
values versus the filling factor in 1D, 2D, and 3D are well approximated by a
simple analytical function. We also discuss the condition for determining the
transition point from a perspective of the instanton method.Comment: 6 pages, 6 figures, 2 table
W_\infty and w_\infty Gauge Theories and Contraction
We present a general method of constructing Winf and winf gauge theories in
terms of d+2 dimensional local fields. In this formulation the \Winf gauge
theory Lagrangians involve non-local interactions, but the winf theories are
entirely local. We discuss the so-called classical contraction procedure by
which we derive the Lagrangian of winf gauge theory from that of the
corresponding Winf gauge theory. In order to discuss the relationship between
quantum Winf and quantum winf gauge theory we solve d=1 gauge theory models of
a Higgs field exactly by using the collective field method. Based on this we
conclude that the Winf gauge theory can be regarded as the large N limit of the
corresponding SU(N) gauge theory once an appropriate coupling constant
renormalization is made, while the winf gauge theory cannot be.Comment: 21 pages, plain Te
Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
Collective field theory for Calogero model represents particles with
fractional statistics in terms of hydrodynamic modes -- density and velocity
fields. We show that the quantum hydrodynamics of this model can be written as
a single evolution equation on a real holomorphic Bose field -- quantum
integrable Benjamin-Ono equation. It renders tools of integrable systems to
studies of nonlinear dynamics of 1D quantum liquids.Comment: 5 pages, 1 figur
Phase Transition in Asymmetrical Superfluids I: Equal Fermi Surfaces
In this paper, we study phase transitions in asymmetrical fermion
superfluids. In this scenario, the candidates to form pair are particles with
mismatched masses and chemical potentials. We derive an expression for the
critical temperature in terms of the gap and masses (or chemical potentials)
when the constraint of equal Fermi surfaces is imposed.Comment: RevTex, 11 pages, 2 figures, typos corrected and an appendix added,
accepted for publication in Phys. Rev.
- …