Chern–Simons particles with nonstandard gravitational interaction

The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity is extended to include Abelian or non-Abelian charges coupled to Chern–Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern–Simons particles coupled, in a reparameterization invariant way, to a translational Chern–Simons action. The quantum 2-body problem is described by a nonstandard Schr?dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels. Received: 16 March 2001 / Published online: 13 June 2001     

Bridge between Abelian and non-Abelian fractional quantum Hall states

We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that K-component Halperin wave functions may be a common basis for both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.     

Effect of Landau level mixing on braiding statistics

We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of Abelian and non-Abelian quantum Hall states. While path dependent geometric phases can perturb the Abelian part of the statistics, we find that the non-Abelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles.     

Renormalization group and infrared behaviour in theories with coupled massless fields

The renormalization-group method is applied to investigate the infrared singularities in gauge theories with Abelian or non-Abelian symmetry, involving both massive and massless fermions. In the Abelian gauge model the infrared structures of massive and massless fermion propagators and of a massive fermion form factor are found. In the non-Abelian gauge model (quantum chromodynamics) the infrared behaviour of a massless gluon propagator and a massive quark form factor is considered in the logarithmic approximation.     

Physics on lattice

A short review of physical results obtained recently in lattice gluodynamics and lattice QCD is given. The topics are: formation and breaking of the confining string, spectrum of hadrons, QCD at finite temperature, monopoles and vortices in Abelian and non-Abelian gauge theories.     

Metal-insulator transition revisited for cold atoms in non-Abelian gauge potentials

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.     

Induced Chern-Simons Term in Three-Dimensional Space at High Temperature

Perturbative calculations of the high temperature ground-state axial vector current of fermion fields coupled to gauge fields lead to an appearance of an additional anomalous Chern-Simons topological mass term in three-dimensional effective action. In Abelian case contributions come only from the vacuum polarization graph, and in non-Abelian case contributions come from the vacuum polarization graph and the two triangle graphs.     

Edge states for quantum Hall droplets in higher dimensions and a generalized WZW model

We consider quantum Hall droplets on complex projective spaces with a combination of Abelian and non-Abelian background magnetic fields. Carrying out an analysis similar to what was done for Abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess–Zumino–Witten (WZW) theory generalized to higher dimensions.     

A covariant approach to gauged 2D self-dual fields

We obtain a non-Abelian version of a theory involving vector and tensor gauge fields interacting via a massive topological coupling, besides the nonminimun one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to make compatible gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case.     

There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group

We prove that there are no magnetically charged particle-like solutions for any model with an Abelian residual group in Einstein Yang-Mills, but for the non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.     

Global charges of stationary non-Abelian black holes

We consider stationary axially symmetric black holes in SU(2) Einstein-Yang-Mills-dilaton theory. We present a mass formula for these stationary non-Abelian black holes, which also holds for Abelian black holes. The presence of the dilaton field allows for rotating black holes, which possess nontrivial electric and magnetic gauge fields, but do not carry a non-Abelian charge. We further present a new uniqueness conjecture.     

Non-Abelian Gauge Theory in the Lorentz Violating Background

In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.     

Heavy quarkonia in a stochastic vacuum

We investigate Green functions for heavy quarkonia in a stochastic vacuum. We derive rigorous results for an Abelian model and expressions for the non-Abelian case which are suited for phenomenological analysis.     

Perturbative QED and QCD at finite temperatures and densities

The finite temperature and density QED and QCD are discussed from the perturbative viewpoint. A comparison between Abelian QED and non-Abelian QCD is made at every step. The calculation of the thermodynamic potential is performed up to ² In, allowing the masses of the fermions to be arbitrary. The equation of state for QCD plasma is obtained and the phase transition to the hadronic phase is discussed.     

On the short-distance potential in confining theories

The structure of leading nonperturbative corrections to the static Coulomb potential at small distances in Abelian and non-Abelian theories is analyzed. Related problems of validity of the Dirac quantization condition for running charges in Abelian theory and significance of the quantity 〈A²〉 are briefly discussed.     

Higgs type excitations in cold atom systems

Higgs type excitations are the excitations which give mass to particles. The Higgs type excitations has a critical role both in particle physics and condensed matter physics. In particle physics, the suspected Higgs boson has been found by the Large Hadron Collider (LHC) in 2012. In condensed matter physics, the Higgs type excitations relate to order phase of the system. In this review, we present an overview of recent studies on the Higgs type excitations both in non-interacting and interacting cold atom systems. First, in non-interacting cold atom system, by synthesizing artificial non-Abelian gauge potential, we demonstrate that when a non-Abelian gauge potential is reduced to Abelian potential, the Abelian part constructs spin-orbit coupling, and the non-Abelian part emerges Higgs excitations. Secondly, the Higgs excitations which are the reputed Higgs amplitude mode in interacting cold atom system are discussed. We review the theoretical model and the experimental detection of Higgs amplitude mode in two dimensional superfluid. The observation of both Higgs type excitations in real experiments are also discussed.     

Engineering complex topological memories from simple Abelian models

In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviors. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. The so-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.     

Quaternion-Octonion Analyticity for Abelian and Non-Abelian Gauge Theories of Dyons

Einstein-Schrödinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex, quaternion and octonion spaces in internal gauge groups are shown to describe the consistent field equations and generalized Dirac equation of dyons. It is also shown that quaternion and octonion representations extend the so-called unified theory of gravitation and electromagnetism to the Yang-Mill’s fields leading to two SU(2) gauge theories of internal spaces due to the presence of electric and magnetic charges on dyons.     

Nonadiabatic geometric phase in quaternionic Hilbert space

We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space.     

Berry phase generation and measurement in a single trapped ion

In this work, we propose a new design of an ion trap which can enable us to generate state specific Berry phase for a single trapped ion. This allows the study of the underlying Abelian and non-Abelian gauge symmetries and could also have significant implications in quantum computation.