Related papers: "Peireles Substitution" and Chern-Simons Quantum M…
The method of the Peierls substitution in studying the magnetic subband structure of a hexagonal lattice is re-examined. Several errors in the formalism of a couple of recent papers are pointed out and rectified so as to describe the effect…
We give an elementary derivation of the chiral magnetic effect based on a strong magnetic field lowest-Landau-level projection in conjunction with the well-known axial anomalies in two- and four-dimensional space-time. The argument is…
The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The…
Composite fermion wavefuctions have been used to describe electrons in a strong magnetic field. We show that the polynomial part of these wavefunctions can be obtained by applying a normal ordered product of suitably defined annihilation…
A generalized Peierls substitution which takes into account a Berry phase term must be considered for the semiclassical treatment of electrons in a magnetic field. This substitution turns out to be an essential element for the correct…
In this short article we introduce the mathematical framework of the principle of the fermionic projector and set up a variational principle in discrete space-time. The underlying physical principles are discussed. We outline the connection…
We study some aspects of recent proposals to use the noncommutative Chern-Simons theory as an effective description of some planar condensed matter models in strong magnetic fields, such as the Quantum Hall Effect. We present an alternative…
We revisit the celebrated Peierls-Onsager substitution employing the magnetic pseudo-differential calculus for weak magnetic fields with no spatial decay conditions, when the non-magnetic symbols have a certain spatial periodicity. We show…
We concisely derive chiral magnetic effect through Wigner function approach for chiral fermion system. Then we derive chiral magnetic effect through solving the Landau levels of chiral fermions in detail. The procedures of second…
Hamiltonian models based on a localized basis set are widely used in condensed matter physics, as, for example, for the calculation of electronic structures or transport properties. The presence of a weak and homogeneous magnetic field can…
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. The book begins with a brief review of relativity,…
An effective Hamiltonian for spinless electrons in the lowest Landau level (LLL) close to half filling is derived. As opposed to the treatment in standard Chern-Simons theories (CS) we first project to the LLL and only then apply a…
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. The book begins with a brief review of relativity,…
The "principle of the fermionic projector" provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. The book begins with a brief review of relativity,…
By considering the area preserving geometric transformations in the configuration space of electrons moving in the lowest Landau level (LLL) we arrive at the Chern-Simons type Lagrangian. Imposing the LLL condition, we get a scheme with the…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…
We consider a (2+1)-dimensional modified electrodynamics endowed with terms that are either Lorentz-invariant or Lorentz-violating and involve an ever increasing number of derivatives. Our construction relies on U(1) gauge invariance and…
We quantize a generalized electromagnetism in 2 + 1 dimensions which contains a higher-order derivative term by using Dirac's method. By introducing auxiliary fields we transform the original theory in a lower-order derivative one which can…
The planar quantum dynamics of a neutral particle with a magnetic dipole moment in the presence of electric and magnetic fields is considered. The criteria to establish the planar dynamics reveal that the resulting nonrelativistic…
We propose a fermion Chern-Simons field theory describing two- dimensional electrons in the lowest Landau level. This theory is constructed with a complete set of states, and the lowest Landau level constraint is enforced through a…