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

Reminiscences

Reminiscences of Bunji Sakita.Comment: Published in "A Quest for Symmetry," Selected Works of Bunji Sakita. Eds.: Keiji Kikkawa, Miguel Virasoro, Spenta Wadia. Published by World Scientifi

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

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

The role of chiefs in peacebuilding in Port Vila

In contrast to the democratic system of government established at independence, the chiefly system in Vanuatu has claimed and now possesses widespread support for its work at the community level. Chiefs are regarded as the key to community harmony and, although Vanuatu is currently experiencing a period of relative stability, underlying social tensions contribute to the high level of importance placed on strong community leadership. Chiefs in Vanuatu have demonstrated their willingness and ability to adapt to changing environments - since colonisation, chiefship has evolved and new chiefly structures have been developed. In the capital of Port Vila especially, chiefs have shown themselves to be resilient to the forces of urbanisation and globalisation. However as the holders of custom, they face a number of unique challenges for which their own systems of governance may not provide ready solutions. Through a discussion on the response of chiefs to the riots that occurred in Port Vila in 1998 and 2007, this paper explores some of the issues currently facing chiefs in Vanuatu’s capita city, Port Vila. Extending the notion that chiefs are responsible for community harmony and well-being, the paper discusses the role of chiefs within the broader framework of development.AusAI

The effective action for edge states in higher dimensional quantum Hall systems

We show that the effective action for the edge excitations of a quantum Hall droplet of fermions in higher dimensions is generically given by a chiral bosonic action. We explicitly analyze the quantum Hall effect on complex projective spaces ${\bf CP}^k$ with a U(1) background magnetic field. The edge excitations are described by abelian bosonic fields on $S^{2k-1}$ with only one spatial direction along the boundary of the droplet relevant for the dynamics. Our analysis also leads to an action for edge excitations for the case of the Zhang-Hu four dimensional quantum Hall effect defined on $S^4$ with an SU(2) background magnetic field, using the fact that ${\bf CP}^3$ is an $S^2$ bundle over $S^4$.Comment: 22 pages, LaTeX, discussion on nature of edge states for S^4 added to section 5, final version to appear in Nucl. Phys.

On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions

An analysis of how the mass gap could arise in pure Yang-Mills theories in two spatial dimensions is givenComment: 10 pages, plain Te

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