Related papers: Nonminimal planar electrodynamics modified by high…
Modified dispersion relations (MDRs) and noncommutative geometries are phenomenological models of Planck-scale corrections to relativistic kinematics, motivated by several approaches to quantum gravity. High-energy astrophysical…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
We extend topologically massive electrodynamics, both by adding a higher derivative action to cast the entire three-term model in Chern-Simons (CS) form, and by embedding it in an AdS background. It can then be written as the sum of two CS…
For two-dimensional topological insulators, the integer and intrinsic (without external magnetic field) quantum Hall effect is described by the gauge anomalous (2+1)-dimensional [2+1d] Chern-Simons (CS) response for the background gauge…
This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…
We survey a new approach to the duality-invariant systems of nonlinear electrodynamics, based on introducing auxiliary bi-spinor fields. In this approach, the entire information about the given self-dual system is encoded in the U(1)…
Quantum oscillation phenomena, in conventional 2-dimensional electron systems and in the fractional quantum Hall effect, are usually treated in the Lifshitz-Kosevich formalism. This is justified in three dimensions by Luttinger's expansion,…
We construct, using the supersymplectic framework of Berezin, Kostant and others, two types of supersymmetric extensions of the Schr\"odinger algebra (itself a conformal extension of the Galilei algebra). An `$I$-type' extension exists in…
We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional…
We calculate the effective electromagnetic Lagrangian up to the lowest-order corrections in the derivatives for two fermionic systems of interest in condensed matter physics in the linearized approximation of the tight-binding Hamiltonian…
Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table~1). Souriau's construction applied to the two-parameter central extension of the planar Galilei…
A Chern--Simons system in $2+1$ dimensions invariant under local Lorentz rotations, $SU(2)$ gauge transformations, and local $\mathcal{N}=2$ supersymmetry transformations is proposed. The field content is that of $(2+1)$-gravity plus an…
The Schr\"odinger-Newton (SN) equation introduces a nonlinear self-gravitational term to the standard Schr\"odinger equation, offering a paradigmatic model for semiclassical gravity. However, the small deviations it predicts from standard…
We present a geometrical formulation of nonlinear electrodynamics by expressing its principal symbol as an optical metric-induced object. Under the assumption of no birefringence, we show that the evolution of linear perturbations can be…
We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle $FLM\to LM$ over the loop space of a Riemannian manifold $M$. Chern-Simons forms are…
The problem of finding all possible effective field theories for the quantum Hall effect is closely related to the problem of classifying all possible modular invariant partition functions for the algebra $u(1)^m$, as was argued recently by…
We perform the complete bosonization of 2+1 dimensional QED with one fermionic flavor in the Hamiltonian formalism. The fermion operators are explicitly constructed in terms of the vector potential and the electric field. We carefully…
In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of…
A non-relativistic version of the 2+1 dimensional gauged Chern-Simons O(3) sigma model, augmented by a Maxwell term, is presented and shown to support topologically stable static self-dual vortices. Exactly like their counterparts of the…
Vortices the $SO(2)$ gauged planar Skyrme model, with a) only Maxwell, b) only Chern-Simons, and c) both Maxwell and Chern-Simons dynamics are studied systematically. In cases a) and b), where both models feature a single parameter…