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We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective classical manifold associated with two-particle bosonic and fermionic coherent states, we show how their exchange statistics is reflected in the symplectic form of the manifold. We demonstrate the classical analogues of exclusion or bunching behavior expected in such states by studying their trajectories in various quadratic potentials. Our examples are two-particle coherent states in one dimension and two-particle vortex motion in the lowest Landau level. We finally compare and contrast our results with previous simulations of the full quantum system, and with existing results on the geometric interpretations of quantum mechanics., Comment: 36 pages, 13 figures, 1 Appendix 2 Supplementary files

We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global anomalies. We illustrate the theory with examples such as quantum Hall liquids, Fermi liquids, Weyl semi-metals, topological insulators and topological superconductors. The required background is basic knowledge of quantum field theory, including fermions and gauge fields, and some familiarity with path integral and functional methods. Some knowledge of topological phases of matter is helpful, but not necessary., Comment: Lecture notes. 148 pages, 24 figures. v2: Minor typos fixed and some references added

We present a field theoretic variant of the Wilczek - Greiter adiabatic approach to Quantum Hall liquids. Specifically, we define a Chern-Simons-Maxwell theory such that the flux-attachment mean field theory is exact in a certain limit. This permits a systematic way to justify a variety of useful approximate approaches to these problems as constituting the first term in a (still to be developed) systematic expansion about a solvable limit., Comment: In version 2 eq. A.1 is corrected, as well as several typos. One reference is added

We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences. By a generalized "flux attachment" construction we extend the Ginzburg-Landau-Chern-Simons composite boson theory to states obtained by both quasielectron and quasihole condensation, and express the corresponding wave functions as correlators in conformal field theories. This yields a precise identification of the relativistic scalar fields entering these correlators in terms of the original electron field., Comment: Submission to SciPost; added comments and references

We consider a number of effects due to the interplay of superconductivity, electromagnetism and elasticity, which are unique for thin membranes of layered chiral superconductors. Some of them should be within the reach of present technology, and could be useful for characterizing materials. More speculatively, the enriched control of Josephson junctions they afford might find useful applications., Comment: published version

In this paper we use a close connection between the coupled wire construction (CWC) of Abelian quantum Hall states and the theory of composite bosons to extract the Laughlin wave function and the hydrodynamic effective theory in the bulk, including the Wen-Zee topological action, directly from the CWC. We show how rotational invariance can be recovered by fine-tuning the interactions. A simple recipe is also given to construct general Abelian quantum Hall states desceibed by the multi-component Wen-Zee action., Comment: 15 pages, 5 figures

We demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. This geometric Meissner effect provides an unequivocal signature of chiral super- conductivity, which could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of zero-energy Majorana modes.

We derive an effective two-dimensional low-energy theory for thin superconducting films coupled to a three-dimensional fluctuating electromagnetic field. Using this theory we discuss plasma oscil- lations, interactions between charges and vortices and extract the energy of a vortex. Having found that the effective theory properly describes the long distance physics, we then use it to investigate to what extent the superconducting film is a topologically ordered phase of matter., Comment: Published, 13 pages, 1 figure

In this paper, we investigate the edge Majorana modes in the simplest possible $p{}_{x}+ip_{y}$ superconductor defined on surfaces with different geometry - the annulus, the cylinder, the M\"obius band and a cone (by cone we mean a cone with the tip cut away so it is topologically equivalent to the annulus and cylinder)- and with different configuration of magnetic fluxes threading holes in these surfaces. In particular, we shall address two questions: Given that, in the absence of any flux, the ground state on the annulus does not support Majorana modes, while the one on the cylinder does, how is it possible that the conical geometry can interpolate smoothly between the two? Given that in finite geometries edge Majorana modes have to come in pairs, how can a $p{}_{x}+ip_{y}$ state be defined on a M\"obius band, which has only one edge? We show that the key to answering these questions is that the ground state depends on the geometry, even though all the surfaces are locally flat. In the case of the truncated cone, there is a non-trivial holonomy, while the non-orientable M\"obius band must necessarily support a domain wall.

The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the thirty years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states, and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of nonabelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments., Comment: added section on experimental status, 59 pages+references, 3 figures

Using methods based on conformal field theory, we construct model wave functions on a torus with arbitrary flat metric for all chiral states in the abelian quantum Hall hierarchy. These functions have no variational parameters, and they transform under the modular group in the same way as the multicomponent generalizations of the Laughlin wave functions. Assuming the absence of Berry phases upon adiabatic variations of the modular parameter $\tau$, we calculate the quantum Hall viscosity and find it to be in agreement with the formula, given by Read, which relates the viscosity to the average orbital spin of the electrons. For the filling factor $\nu=2/5$ Jain state, which is at the second level in the hierarchy, we compare our model wave function with the numerically obtained ground state of the Coulomb interaction Hamiltonian in the lowest Landau level, and find very good agreement in a large region of the complex $\tau$-plane. For the same example, we also numerically compute the Hall viscosity and find good agreement with the analytical result for both the model wave function and the numerically obtained Coulomb wave function. We argue that this supports the notion of a generalized plasma analogy that would ensure that wave functions obtained using the conformal field theory methods do not acquire Berry phases upon adiabatic evolution.

We propose a topological field theory for a spin-less two-dimensional chiral superconductor that contains fundamental Majorana fields. Due to a fermionic gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only at magnetic vortex cores, and on edges. We argue that these modes have the topological properties pertinent to a p-wave superconductor including the non-abelian braiding statistics, and support this claim by calculating the ground state degeneracy on a torus. We also briefly discuss the connection to the Moore-Read Pfaffian quantum Hall state, and extensions to the spinful case and to three-dimensonal topological superconductors., Comment: 6 pages, Some explanatory text added, and the discussion of degeneracy on the torus reformulated

The abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-abelian states emanating from the {\nu} = 5/2 Moore-Read state in the second Landau level. Extending a recently developed formalism for hierarchical quasihole condensation, we present a theory that allows for the explicit construction of the ground state wave function, as well as its quasiparticle excitations, for any state based on the abelian hierarchy. We relate our construction to structures in rational conformal field theory and stress the importance of using coherent state wave functions which allows us to formulate an extension of the bulk - edge correspondence that was conjectured by Moore and Read. Finally, we study the proposed ground state wave functions in the limiting geometry of a thin torus and argue that they coincide with the known exact results., Comment: 18 pages

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates., Comment: 16 pages

We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise., Comment: 4 pages, 3 figures

It is now established that the state proposed by Tao and Thouless for the fractional quantum Hall effect in 1983, shortly after Laughlin's work, is the ground state in the so-called Tao-Thouless limit, and that it is adiabatically connected to the Laughlin state. We review the interesting history of the Tao-Thouless state, and its generalizations, and discuss its relevance and shortcomings. In particular, we calculate the exclusion statistics of quasiparticles in the Tao-Thouless limit and point out a principal difficulty which prevents calculation of the fractional exchange statistics in this limit., Comment: 6 pages, 2 figures

We examine charge fractionalization by chiral separation in a one-dimensional fermion system described by Luttinger liquid theory. The focus is on the question of whether the fractional charges are quantum mechanically sharp, and in the analysis we make a distinction between the global charge, which is restricted by boundary conditions, and the local charge where a background contribution is subtracted. We show, by way of examples, that fractional charges of arbitrary values, all which are quantum mechanically sharp, can be introduced by different initial conditions. Since the system is gapless, excitations of arbitrary low frequency contribute to the fluctuations, it is important to make a precise definition of sharp charges, and this we we do by subtraction of the ground state contribution. We very briefly comment on the relevance of our analysis for proposed experiments., Comment: One reference updated

In the conformal field theory (CFT) approach to the quantum Hall effect, the multi-electron wave functions are expressed as correlation functions in certain rational CFTs. While this approach has led to a well-understood description of the fractionally charged quasihole excitations, the quasielectrons have turned out to be much harder to handle. In particular, forming quasielectron states requires non-local operators, in sharp contrast to quasiholes that can be created by local chiral vertex operators. In both cases, the operators are strongly constrained by general requirements of symmetry, braiding and fusion. Here we construct a quasielectron operator satisfying these demands and show that it reproduces known good quasiparticle wave functions, as well as predicts new ones. In particular we propose explicit wave functions for quasielectron excitations of the Moore-Read Pfaffian state. Further, this operator allows us to explicitly express the composite fermion wave functions in the positive Jain series in hierarchical form, thus settling a longtime controversy. We also critically discuss the status of the fractional statistics of quasiparticles in the Abelian hierarchical quantum Hall states, and argue that our construction of localized quasielectron states sheds new light on their statistics. At the technical level we introduce a generalized normal ordering, that allows us to "fuse" an electron operator with the inverse of an hole operator, and also an alternative approach to the background charge needed to neutralize CFT correlators. As a result we get a fully holomorphic CFT representation of a large set of quantum Hall wave functions., Comment: minor changes, published

The quasiparticles in Quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could in principle be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes both in Abelian and non-Abelian QH states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons, and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state., Comment: figure added

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $\nu=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $\nu=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions., Comment: 9 pages

We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at e.g. $\nu = 4/11$. The techniques we use constitute a nontrivial extension of the conformal field theory methods developed earlier to construct the corresponding wave functions in disc geometry.

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan {\it et. al.}, and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states., Comment: 4 pages, 2 figures. Published

We analyze the Moore-Read Pfaffian state on a thin torus. The known six-fold degeneracy is realized by two inequivalent crystalline states with a four- and two-fold degeneracy respectively. The fundamental quasihole and quasiparticle excitations are domain walls between these vacua, and simple counting arguments give a Hilbert space of dimension $2^{n-1}$ for $2n-k$ holes and $k$ particles at fixed positions and assign each a charge $\pm e/4$. This generalizes the known properties of the hole excitations in the Pfaffian state as deduced using conformal field theory techniques. Numerical calculations using a model hamiltonian and a small number of particles supports the presence of a stable phase with degenerate vacua and quarter charged domain walls also away from the thin torus limit. A spin chain hamiltonian encodes the degenerate vacua and the various domain walls., Comment: 4 pages, 1 figure. Published, minor changes

We show that the quantum Hall wave functions for the ground states in the Jain series can be exactly expressed in terms of correlation functions of local vertex operators, V_n, corresponding to composite fermions in the n:th composite-fermion (CF) Landau level. This allows for the powerful mathematics of conformal field theory to be applied to the successful CF phenomenology. Quasiparticle and quasihole states are expressed as correlators of anyonic operators with fractional (local) charge, allowing a simple algebraic understanding of their topological properties that are not manifest in the CF wave functions., Comment: 1 color figure; new result on exact correspondence between CF wave functions and CFT correlators included; presentation made less technical; some references changed

We show how to incorporate fractionally charged quasielectrons in the finite quantum Hall matrix model.The quasielectrons emerge as combinations of BPS solitons and quasiholes in a finite matrix version of the noncommutative $\phi^4$ theory coupled to a noncommutative Chern-Simons gauge field. We also discuss how to properly define the charge density in the classical matrix model, and calculate density profiles for droplets, quasiholes and quasielectrons., Comment: 15 pages, 9 figures

We develop an exact generalized Bogoliubov transformation for the spin 3/2 Hubbard model with large anti-Hunds rule coupling near half filling. Since our transformation is unitary, we can thereafter employ standard approximate mean field theory methods in the full Hilbert space to analyze the doped Mott insulator, in contrast to a conventional approach based on truncated Hilbert spaces complemented with hard core constraints. The ground state at exactly half filling is an insulating (Mott) singlet, and according to our analysis a non-Fermi liquid order parameter $ \Delta $ usually associated with extended s-wave superconductivity, will appear self-consistently as soon as a finite density $ n $ holes are introduced. The non-Fermi liquid behavior is a consequence of the nonlinear nature of the unitary transformation mapping the Mott singlet state to a Fock vacuum which introduces anomalous terms such as $\Delta n$ in the effective Lagrangian. Our analysis uses an approach that generalizes readily to multi-band Hubbard models and could provide a mechanism whereby a non-Fermi liquid order parameter proportional to density is developed in Mott insulators with locally entangled ground states. For more complicated systems, such an order parameter could coexist naturally with a variety of other order parameters.

We revisit a venerable question: what is the nature of the ordering in a superconductor? We find that the answer is properly that the superconducting state exhibits topological order in the sense of Wen, i.e. that while it lacks a local order parameter, it is sensitive to the global topology of the underlying manifold and exhibits an associated fractionalization of quantum numbers. We show that this perspective unifies a number of previous observations on superconductors and their low lying excitations and that this complex can be elegantly summarized in a purely topological action of the ``$BF$'' type and its elementary quantization. On manifolds with boundaries, the $BF$ action correctly predicts non-chiral edge states, gapped in general, but crucial for fractionalization and establishing the ground state degeneracy. In all of this the role of the physical electromagnetic fields is central. We also observe that the $BF$ action describes the topological order in several other physically distinct systems thus providing an example of topological universality.

We study topological aspects of a compact lattice superconductor, and show that the characteristic energy splitting, $\Delta$, between almost degenerate ground states, is simply related to a novel order parameter $\tilde W$, which is closely related to large Wilson loops. Using Monte Carlo methods, we study the scaling properties of $\tilde W$ close to the deconfining phase transition, and conclude that $\Delta \sim e^{-L/\xi}$, where $L$ is the size of the system, thus giving quantitative support to the vortex tunneling scenario proposed by Wen., Comment: 7 pages, 3 figures

We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional ``photon fluid'' confined in a Fabry-Perot resonator. With the atoms modelled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the ``bare'' strength of the anharmonic term. The resulting expression for the non-linear Kerr susceptibility, is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity., Comment: 25 pages (revtex4), including 2 figures

We extend the quantum Hall matrix model to include couplings to external electric and magnetic fields. The associated current suffers from matrix ordering ambiguities even at the classical level. We calculate the linear response at low momenta -- this is unambigously defined. In particular, we obtain the correct fractional quantum Hall conductivity, and the expected density modulations in response to a weak and slowly varying magnetic field. These results show that the classical quantum Hall matrix models describe important aspects of the dynamics of electrons in the lowest Landau level. In the quantum theory the ordering ambiguities are more severe; we discuss possible strategies, but we have not been able to construct a good density operator, satisfying the pertinent lowest Landau level commutator algebra., Comment: 12 pages, no figures; a logical error below the proposed density operator (46) in version 1 is corrected, and the claim that this density operator satisfy the magnetic algebra (2) is withdrawn. Some formulations have been changed and a few misprints corrected

Magnetically-trapped atoms in Bose-Einstein condensates are spin polarized. Since the magnetic field is inhomogeneous, the atoms aquire Berry phases of the Aharonov-Bohm type during adiabatic motion. In the presence of an eletric field there is an additional Aharonov-Casher effect. Taking into account the limitations on the strength of the electric fields due to the polarizability of the atoms, we investigate the extent to which these effects can be used to induce rotation in a Bose-Einstein condensate., Comment: 5 pages, 2 ps figures, RevTex

We couple the noncommutative Chern-Simons theory describing the fractional quantum Hall effect to external magnetic and electric potentials, and derive expressions for charge and current densities. To lowest non-trivial order the density operator satisfies the commutator algebra characteristic of the lowest Landau level. We take this as a strong indication that the theory correctly describes point particles in a strong magnetic field. We also obtain the correct QH response to a constant electric field, and density modulations in response to a weak variable magnetic field., Comment: 4 pages, revised version; eq.(14) and one ref. added

We briefly explain the notion of exclusion statistics and in particular discuss the concept of an ideal exclusion statistics gas. We then review a recent work where it is demonstrated that a {\em two-dimensional} Bose gas with repulsive delta function interactions obeys ideal exclusion statistics, with a fractional parameter related to the interaction strength., Comment: 10 pages, RevTeX. Proceedings of the Salerno workshop "Theory of Quantum Gases and Quantum Coherence", to appear in a special issue of J.Phys. B, Dec. 2001

We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion statistics gas., Comment: 3 pages; minor changes in notation; typos corrected

We present a general method to derive the classical mechanics of a system of identical particles in a way that retains information about quantum statistics. The resulting statistical mechanics can be interpreted as a classical version of Haldane's exclusion statistics., Comment: Latex, 4 pages

Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical particles in the lowest Landau level, and vortices in the Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical} statistical mechanics is shown to be a nontrivial classical limit of Haldane's exclusion statistics., Comment: 40 pages, Latex

We exploit the analogy with the Quantum Hall (QH) system to study weakly interacting bosons in a harmonic trap. For a $\delta$-function interaction potential the ``yrast'' states with $L\ge N(N-1)$ are degenerate, and we show how this can be understood in terms of Haldane exclusion statistics. We present spectra for 4 and 8 particles obtained by numerical and algebraic methods, and demonstrate how a more general hard-core potential lifts the degeneracies on the yrast line. The exact wavefunctions for N=4 are compared with trial states constructed from composite fermions (CF), and the possibility of using CF-states to study the low L region at high N is discussed., Comment: 6 pages, including 4 figures and 3 tables

Starting from recently proposed bosonic mean field theories for fully and partially polarized quantum Hall states, we construct corresponding effective low energy theories for the edge modes. The requirements of gauge symmetry and invariance under global O(3) spin rotations, broken only by a Zeeman coupling, imply boundary conditions that allow for edge spin waves. In the generic case, these modes are chiral, and the spin stiffness differs from that in the bulk. For the case of a fully polarized $\nu=1$ state, our results agree with previous Hartree-Fock calculations., Comment: 15 pages (number of pages has been reduced by typesetting in RevTeX); 2 references added

We propose a new effective field theory for partially polarized quantum Hall states. The density and polarization for the mean field ground states are determined by couplings to two Chern-Simons gauge fields. In addition there is a $\sigma$-model field, $\mh$, which is necessary both to preserve the Chern-Simons gauge symmetry that determines the correlations in the ground state, and the global SU(2) invariance related to spin rotations. For states with non zero polarization, the low energy dynamics is that of a ferromagnet. In addition to spin waves, the spectrum contains topological solitons, or skyrmions, just as in the fully polarized case. The electric charge of the skyrmions is given by $Q_{el}=\nu P Q_{top}$, where $\nu$ is the filling fraction, $P$ the magnitude of the polarization, and $Q_{top}$ the topological charge. For the special case of full polarization, the theory involves a single scalar field and a single Chern-Simons field in addition to the $\sigma$-model field, $\mh$. We also give a heuristic derivation of the model lagrangians for both full and partial polarization, and show that in a mean field picture, the field $\mh$ is necessary in order to take into account the Berry phases originating from rotations of the electron spins., Comment: RevTex, 9 pages

Assuming that gluon condensates are important even above the deconfining phase transition, we develop a model for the dilepton yield from a quark gluon plasma. Using a simple fire ball description of a heavy ion collision, and various estimates of the strengths of the gluon condensates, we compare our predicted dilepton yields with those observed in the CERES and HELIOS experiments at CERN. The simple model gives an adequate description of the data, and in particular it explains the observed considerable enhancement of the yield in the low mass region., Comment: 7 pages, 6 figures, reference added

We use the background field method along with a special gauge condition, to derive the hard thermal loop effective action in a simple manner. The new point in the paper is to relate the effective action explicitly to the S-matrix from the onset., Comment: 11 pages, Latex; lost text after sect. 2 reinserted

We use dimensional reduction techniques to relate real time finite T correlation functions in (2+1) dimensional QCD to bound state parameters in a generalized 't Hooft model with an infinite number of heavy quark and adjoint scalar fields. While static susceptibilities and correlation functions of the DeTar type can be calculated using only the light (static) gluonic modes, the dynamical correlators require the inclusion of the heavy modes. In particular we demonstrate that the leading T perturbative result can be understood in terms of the bound states of the 2d model and that consistency requires bound state trajectories composed of both quarks and adjoint scalars. We also propose a non-perturbative expression for the dynamical DeTar correlators at small spatial momenta., Comment: 21 pages, Latex, uses axodraw

We consider a two-component quantum Hall system within a Landau-Ginzburg theory with two Chern-Simons gauge fields. From this theory we derive a sigma model covariantly coupled to one Chern-Simons field and find mean field solutions that could describe partially polarized quantum Hall states. The quasiparticles in the original model, which have quantized charge and spin, are described in the covariant sigma model by topological excitations, with the correct quantum numbers. They have finite energy due to the presence of the Chern-Simons field, and closely resemble the skyrmions in the usual non-linear sigma model. For the fully polarized states the spin is no longer quantized, but determined by Coulomb and Zeeman interactions., Comment: 12 pages, RevTeX

We use the dual description proposed by Seiberg to calculate the pressure in the low temperature confined phase of $N=1$ supersymmetric QCD using perturbation theory to $O(g^3_m)$, where $g_m$ is the gauge coupling in the dual theory. Combining this result with the usual high temperature expansion based on asymptotic freedom, we study how the physics in the intermediate temperature regime depends on the relative size of the scale parameters in the two descriptions. In particular we explore the possibility of having a temperature range where both perturbation expansions are valid., Comment: LaTex, 17 pages, Figures included using LaTeX format. Uses uufiles

We construct a field theory for anyons in the lowest Landau level starting from the $N$-particle description, and discuss the connection to the full field theory of anyons defined using a statistical gauge potential. The theory is transformed to free form, with the fields defined on the circle and satisfying modified commutation relations. The Fock space of the anyons is discussed, and the theory is related to that of edge excitations of an anyon droplet in a harmonic oscillator well., Comment: 27 pages (incl. 2 figs.) in standard Latex. Substantially revised version with a section on the connection to Luttinger liquids

Using a loop formulation approach of QCD$_2$, we study the potential between two heavy quarks in the presence of adjoint scalar fields, and demonstrate how 't Hooft's planar rule is manifested in this formulation. Based on some physical assumptions, we argue that large adjoint loops ``confined'' inside an external fundamental one give a Casimir type contribution to the potential energy, while the small loops only renormalize the string tension. We also extend the results to the case of massive adjoint fields., Comment: 24 pages phyzzx (6 figures available upon request), USITP-94-14

We derive an $su(1,1)$ coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to a $su(1,1)$ version of the Holstein-Primakoff transformation., Comment: Latex 6 pages, USITP-94-13

We use arguments taken from the electrodynamics of media to deduce the QCD trace anomaly from the expression for the vacuum energy in the presence of an external color magnetic field., Comment: 18 pages, USITP 94-11