Related papers: Dirac field in $\mathrm{AdS}_2$ and representation…
We use an algebraic approach based on representations of de Sitter group to construct covariant quantum fields in arbitrary dimensions. We study the complementary and the discrete series which correspond to light and massless fields and…
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to…
The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3+1 dimensions where no…
We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak…
Solutions of the Dirac equation for an electron in the Coulomb potential are obtained using operator invariants of the equation, namely the Dirac, Johnson-Lippmann and recently found new invariant. It is demonstrated that these operators…
We study the effect of spatially dependent mass function over the solution of the Dirac equation with the Coulomb potential in the (3+1)-dimensions for any arbitrary spin-orbit $\kappa $ state$.$ In the framework of the spin and pseudospin…
We present a privileged Fock quantization of a massive Dirac field in a closed Friedmann-Robertson-Walker cosmology, partially selected by the criteria of invariance of the vacuum under the symmetries of the field equations, and unitary…
We explore analytical aspects of correlators involving Dirac spinors in $d+1$- dimensional de Sitter space. Adapting the formalism of Sleight and Taronna, we show how to relate processes involving fermions in the in-in formalism to…
We consider the role of boundary conditions in the $AdS_{d+1}/CFT_{d}$ correspondence for the scalar field theory. Also a careful analysis of some limiting cases is presented. We study three possible types of boundary conditions, Dirichlet,…
We investigate the behavior of the Dirac spinor fields in general relativistic high density stellar backgrounds and the possibility of spontaneous spinorization which is analogous to spontaneous scalarization. We consider the model with the…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
We study solutions to the Dirac equation in Minkowski space $\mathbb{R}^{1,d+1}$ that transform as $d$-dimensional conformal primary spinors under the Lorentz group $SO(1,d+1)$. Such solutions are parameterized by a point in $\mathbb{R}^d$…
World spinors are objects that transform w.r.t. double covering group $\bar{Diff}(4,R)$ of the Group of General Coordinate Transformations. The basic mathematical results and the corresponding physical interpretation concerning these,…
We study Discrete Series representations of $SL(2,\mathbb{R})$ with half-integer scaling dimension $\Delta$. At the classical level, we show that these UIRs are realised in the space of mode solutions of spinor fields with imaginary mass…
We use the polar decomposition to describe the Dirac field in terms of an effective spinorial fluid. After reformulating all covariant equations in ``spinorial'' signature $(+ -- )$, we develop a $(1+1+2)$ covariant approach for the Dirac…
Employing the covariant language of two-spinors, we find what conditions a curved Lorentzian spacetime must satisfy for existence of a second order symmetry operator for the massive Dirac equation. The conditions are formulated as existence…
Tensor and matrix formulations of Dirac-K\"ahler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection…
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…
$P$-, $T$-, $C$-transformations of the Dirac field in the de Sitter space are studied in the framework of an automorphism set of Clifford algebras. Finite group structure of the discrete transformations is elucidated. It is shown that $CPT$…
These notes describe representations of the universal cover of $\mathrm{SL}(2,\mathbb{R})$ with a view toward applications in physics. Spinors on the hyperbolic plane and the two-dimensional anti-de Sitter space are also discussed.