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 $D \rightarrow PV$ and $D \rightarrow VV$, 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 $D \rightarrow PP$ 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 ν=1\nu =1 Hall ferromagnet

In this article, we shall focus on the collective dynamics of the fermions in a $\nu = 1$ 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 $m_a\mu_a = m_b\mu_b$ is imposed.Comment: RevTex, 11 pages, 2 figures, typos corrected and an appendix added, accepted for publication in Phys. Rev.