相关论文: Polar form of Dirac fields: implementing symmetrie…

We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some…

In "Part I: Vector Analysis of Spinors", the author studied the geometry of two component spinors as points on the Riemann sphere in the geometric algebra of three dimensional Euclidean space. Here, these ideas are generalized to apply to…

The field equation for a spin 1/2 massive charged particle propagating in spacetimes that are the direct product of 2-dimensional spaces is separated. Moreover, we use this result to attain the separability of the Dirac equation in some…

By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex…

We develop a general scheme to construct integrable systems starting from realizations in symmetric coboundary dynamical Lie algebroids and symmetric coboundary Poisson groupoids. The method is based on the successive use of Dirac reduction…

The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case…

We study the existence of left-invariant harmonic spinors on three-dimensional Lie groups equipped with a left-invariant pseudo-Riemannian metric. An existing formula for the spin Dirac operator acting on left-invariant spinors in the…

Dirac equation for a charged particle in static electromagnetic field is written for special cases of spherically symmetric potentials. Besides the well known Dirac-Coulomb and Dirac-Oscillator potentials, we obtain a relativistic version…

A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…

Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…

We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.

We employ the polar re-formulation of spinor fields to see in a new light their classification into regular and singular spinors, these last also called flag-dipoles, further splitting into the sub-classes of dipoles and flagpoles: in…

We use the Dirac operator method to prove a scalar-mean curvature comparison theorem for spin manifolds which carry iterated conical singularities. Our approach is to study the index theory of a twisted Dirac operator on such singular…

Connection of the invariant Dirac equation over the de Sitter space with irreducible representations of the de Sitter group is ascertained. The set of solutions of this equation is obtained in the form of the product of two different…

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…

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…

Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac…

In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By…

We investigate to construct a conformal scattering theory of the spin-$1/2$ massless Dirac equation on the Kerr spacetime by using the conformal geometric method and under an assumption on the pointwise decay of the Dirac field. In…