Related papers: Representation-independent manipulations with Dira…
It is pointed out that there are gauge-dependent and gauge-independent spinors within the little-group framework for internal space-time symmetries of massless particles. It is shown that two of the $SL(2,c)$ spinors are invariant under…
Let $\mathfrak g$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak g$ to be rectangular and completely classify faithful rectangular representations. As an application, we…
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…
In a Minkowski spacetime, one may transform the Dirac wave function under the spin group, as one transforms coordinates under the Poincar\'e group. This is not an option in a curved spacetime. Therefore, in the equation proposed…
We consider several classes of symmetries of the Dirac Hamiltonian in 3+1 dimensions, with axially-deformed scalar and vector potentials. The symmetries include the known pseudospin and spin limits and additional symmetries which occur when…
A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…
Modifications of Dirac operators in supergravity flux backgrounds are considered. Modified spin curvature operators and squares of modified Dirac operators corresponding to Schr\"odinger-Lichnerowicz-like formulas are obtained for different…
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
A system in which the free part of the action possesses a gauge symmetry that is not respected by the interacting part presents problems when quantized. We illustrate how the Dirac constraint formalism can be used to address this difficulty…
We show that the class of every primitive indefinite binary quadratic form is naturally represented by an infinite graph (named \c{c}ark) with a unique cycle embedded on a conformal annulus. This cycle is called the spine of the \c{c}ark.…
The so called Inomata-McKinley spinors are a particular solution of the non-linear Heisenberg equation. In fact, free linear massive (or mass-less) Dirac fields are well known to be represented as a combination of Inomata-McKinley spinors.…
Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature…
Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac…
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
Matrix transformations in terms of triangular matrices is the easiest method of evaluating matrix-variate gamma and beta integrals in the real and complex cases. Here we give several procedures of explicit evaluation of gamma and beta…
We introduce a functional that couples the nonlinear sigma model with a spinor field: $L=\int_M[|d\phi|^2+(\psi,\D\psi)]$. In two dimensions, it is conformally invariant. The critical points of this functional are called Dirac-harmonic…
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…
We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second class constraints the Dirac brackets of the proposed theory represent the commutation relations for…
On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of…