Related papers: Super-Symmetric Coupling: Existence and Multiplici…
Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy…
We reexamine the solvable model problem of two static, fundamental quarks interacting with a SU(2) Yang-Mills field on a spatial circle, introduced by Engelhardt and Schreiber. If the quarks are at the same point, the model exhibits a…
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
We provide a framework to compute the dynamics of massive Dirac fermions using holography. To this end we consider two bulk Dirac fermions that are coupled via a Yukawa interaction and propagate on a gravitational background in which a mass…
Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with…
We study the effective action associated to the Dirac operator in two dimensional non-commutative Field Theory. Starting from the axial anomaly, we compute the determinant of the Dirac operator and we find that even in the U(1) theory, a…
Filling-enforced Dirac semimetals, or those required at specific fillings by the combination of crystalline and time-reversal symmetries, have been proposed and discovered in numerous materials. However, Dirac points in these materials are…
Topological superconductors should be able to provide essential ingredients for quantum computing, but are very challenging to realize. Spin-orbit interaction in iron-based superconductors opens the energy gap between the $p$-states of…
In this paper we complete the proof of the existence of multiple solutions (and, in particular, non minimal ones), to the epsilon-Dirichlet problem obtained as a variational problem for the SU(2)-epsilon-Yang Mills functional. This is…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
In this paper we introduce the conformal fractional Dirac operator and its associated fractional spinorial Yamabe problem. We also present a Caffarelli-Silvestre type extension for this fractional operator, allowing us to express it as a…
We study a model in $d = 2 + 1$ space-time dimensions with two sectors. One of them, which can be considered as the visible sector, contains just a $U(1)$ gauge field which acts as a probe for the other (hidden) sector, given by a second…
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
We study the effect of disorder on massless, spinful Dirac fermions in two spatial dimensions with attractive interactions, and show that the combination of disorder and attractive interactions is deadly to the Dirac semimetal phase. First,…
We study a functional that derives from the classical Yang-Mills functional and Born-Infeld theory. We establish its first variation formula and prove the existence of critical points. We also obtain the second variation formula.
In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We use a hypercomplex argument…
We propose a new band engineering scheme on the biphenylene network, a newly synthesized carbon allotrope. First, we investigate the mechanism for the appearance of type II Dirac fermion in a pristine biphenylene network. We show that the…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
Dirac semimetals, with their protected Dirac points, present an ideal platform for realizing intrinsic topological superconductivity. In this work, we investigate superconductivity in a two-dimensional, square-lattice nonsymmorphic Dirac…
The all-orders beta function is used to study disordered Dirac fermions in 2D. The generic strong coupling fixed `points' of anisotropic current-current interactions at large distances are actually isotropic manifolds corresponding to…