Chern-Simons Soliton Dynamics in Modular Parameter Space

We study dynamics of non-relativistic Chern-Simons solitons, both in the absence and in the presence of external fields. We find that a phase, related to the $1$-cocyle of the Galileo group, must be included to give the correct dynamical behavior. We show that interactions among Chern-Simons solitons are mediated by an effective Chern-Simons gauge field induced by the solitons. In the two soliton case, we evaluate analytically the effective interaction Lagrangian, which previously was found numerically.Comment: 10 pages, CTP #224

Noncommuting fields and non-Abelian fluids

The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described.Comment: 16 pp., invited talk at "Renormalization Group and Anomalies in Gravity and Cosmology", Ouro Preto, Brazil, March 2003. Minor typos correcte

Extended Superconformal Galilean Symmetry in Chern-Simons Matter Systems

We study the nonrelativistic limit of the $N=2$ supersymmetric Chern-Simons matter system. We show that in addition to Galilean invariance the model admits a set of symmetries generated by fermionic charges, which can be interpreted as an {\it extended Galilean supersymmetry }. The system also possesses a hidden conformal invariance and then the full group of symmetries is the {\it extended superconformal Galilean} group. We also show that imposing extended superconformal Galilean symmetry determines the values of the coupling constants in such a way that their values in the bosonic sector agree with the values of Jackiw and Pi for which self-dual equation exist. We finally analyze the second quantized version of the model and the two-particle sector.Comment: 32 double-spaced page

Tutorial on Scale and Conformal Symmetries in Diverse Dimensions

We review the relation between scale and conformal symmetries in various models and dimensions. We present a dimensional reduction from relativistic to non-relativistic conformal dynamics.Comment: Addendum added that includes author S.-H. Ho; Sodano Fest, Perugia, Italy, January 201

Comment On Vortices In Chern-Simons And Maxwell Electrodynamics

We compare the vortex-like solutions of two different theories in (2+1) dimensions. In the first a nonrelativistic field self-interacts through a Chern-Simons gauge connection. It is $P$ and $T$ violating. The second is the standard Maxwell scalar electrodynamics. We show that for specific values of some parameters the same vortex-configurations provide solutions for both theories.Comment: 10 pages, Plain Te

Covariant Coordinate Transformations on Noncommutative Space

We show how to define gauge-covariant coordinate transformations on a noncommuting space. The construction uses the Seiberg-Witten equation and generalizes similar results for commuting coordinates.Comment: 11 pages, LaTeX; email correspondence to [email protected]

Chiral solitons from dimensional reduction of Chern-Simons gauged non-linear Schr\"odinger model of FQHE: classical and quantum aspects

The soliton structure of a gauge theory recently proposed to describe chiral excitations in the Fractional Quantum Hall Effect is investigated. A new type of non-linear derivative Schr\"odinger equation emerges as an effective description of the system that supports novel chiral solitons. We discuss the classical properties of solutions with vanishing and non-vanishing boundary conditions (dark solitons) and we explain their relation to integrable systems. The quantum analysis is also addressed in the framework of a semiclassical approximation improved by Renormalization Group arguments.Comment: 39 page, RevTeX, 6 figure