Related papers: Dimensional reduction of the Dirac theory
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism…
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to…
It is shown that the free Dirac equation in spherically symmetric static backgrounds of any dimensions can be put in a simple form using a special version of Cartesian gauge in Cartesian coordinates. This is manifestly covariant under the…
In this paper, two things are done. First, we analyze the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories down to three spacetime dimensions. We show…
Using the language of the Geometric Algebra, we recast the massless Dirac bispinor as a set of Lorentz scalar, bivector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. The spinor's unusual…
The Dirac constraint formalism is used to analyze the first order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that…
We examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the non-relativistic anti-Snyder model which is relevant to deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum…
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic…
We theoretically study the spin susceptibility of Dirac semimetals using the linear response theory. The spin susceptibility is decomposed into an intraband contribution and an interband contribution. We obtain analytical expressions for…
We investigate the (1+1)-dimensional position-dependent mass Dirac equation within the confines of so(2,1) potential algebra by utilizing the character of a spatial varying Fermi velocity. We examine the combined effects of the two when the…
In this work we analyze the zero mode localization and resonances of $1/2-$spin fermions in co-dimension one Randall-Sundrum braneworld scenarios. We consider delta-like, domain walls and deformed domain walls membranes. Beyond the…
A constant magnetic field in 3+1 and 2+1 dimensions is a strong catalyst of dynamical chiral symmetry breaking, leading to the generation of a fermion mass even at the weakest attractive interaction between fermions. The essence of this…
We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle,…
There exists a freedom in a class of four-dimensional electroweak theories proposed by Arkani-Hamed et al. relying on deconstruction and Coleman-Weinberg mechanism. The freedom comes from the winding modes of the link variable (Wilson…
We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially…
In this paper, we study the (1+3) dimensional massive Maxwell-Dirac system in the context of global existence and asymptotic behavior of solutions under the Lorenz gauge condition, as well as the modified and linear scattering phenomena for…
The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown…
Using the parent Lagrangian method together with a dimensional reduction from $D$ to $(D-1)$ dimensions we construct dual theories for massive spin two fields in arbitrary dimensions in terms of a mixed symmetry tensor $T_{A[A_{1}A_{2}...…
We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter $\Delta$, there are two distinct Dirac points…
We extend a previously successful discussion of the constrained Schr\"{o}dinger system through the Dirac--Bergmann algorithm to the case of the Dirac field. In order to follow the analogy, first we discuss the classical Dirac field as a…