Related papers: Conservation of the Dirac Current in Models with a…
We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic…
In this article we prove spin statistics theorem for arbitrary massive (A, B) field in a representation theoretic manner. General Gamma matrices are introduced, and explicit forms for low spin are calculated. Spin sums and twisted spin sums…
We investigate the Cabbibo-Ferrari, two potential approach to magnetic charge coupled to two different complex scalar fields, $\Phi_1$ and $\Phi_2$, each having different electric and magnetic charges. The scalar field, $\Phi_1$, is assumed…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
In this paper, we consider a general twisted-curved space-time hosting Dirac spinors and we take into account the Lorentz covariant polar decomposition of the Dirac spinor field: the corresponding decomposition of the Dirac spinor field…
We give a method which generates sufficient conditions for instability of equilibria for circulatory and gyroscopic conservative systems. The method is based on the Gramians of a set of vectors whose coordinates are powers of the roots of…
The existence of normalizable zero modes of the twisted Dirac operator is proven for a class of static Einstein-Yang-Mills background fields with a half-integer Chern-Simons number. The proof holds for any gauge group and applies to Dirac…
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the…
We reexamine the existence and stability conditions of Dirac points between valence and conduction bands of 3/4 filled $\alpha$-(BEDT-TTF)$_2$I$_3$ conducting plane. We consider the usual nearest neigbhor tight binding model with the seven…
We study f(R)-gravity with torsion in presence of Dirac massive fields. Using the Bianchi identities, we formulate the conservation laws of the theory and we check the consistency with the matter field equations. Further, we decompose the…
We study a confined system of Dirac fermions in the presence of inhomogeneous magnetic field. Splitting the system into different regions, we determine their corresponding energy spectrum solutions. We underline their physical properties by…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
I show that there exist twelve independent Dirac equations for spin 1/2 fermions. The Dirac fields that satisfy these equations can be grouped into six pairs according to the way they transform under continuous space-time transformations.…
We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential…
We investigate how symmetries and conserved quantities relate to the occurrence of the boundary time crystal (BTC) phase in a generalized spin model with Lindblad dissipation. BTCs are a non-equilibrium phase of matter in which the system,…
We demonstrate that spin supercurrents are conserved upon transmission through a conventional superconductor, even in the presence of spin-dependent scattering by impurities with magnetic moments or spin-orbit coupling. This is…
We present gauge-invariant theory of the dynamic inverse spin Hall effect driven by the spin--orbit interaction in metallic systems. Charge conservation is imposed diagrammatically by including vertex corrections. We show the charge current…
The distributed system $\mathcal{S}_D$ described by the Dirac equation is investigated simply as a dynamic system, i.e. without usage of quantum principles. The Dirac equation is described in terms of hydrodynamic variables: 4-flux $j^{i}$,…
Schr\"odinger equation for an electron confined to a two-dimensional strip is considered in the presence of homogeneous orthogonal magnetic field. Since the system has edges, the eigenvalue problem is supplied by the boundary conditions…
We study the deacy and Strichartz estimates for the massive Dirac Hamiltonian in a constant magnetic fields in $\mathbb{R}_t\times\mathbb{R}^2_x$: \begin{equation*} \begin{cases} i\partial_tu(t,x)-\mathcal{D}_Au(t,x)=0, u(0,x)=f,…