Related papers: Axially-Symmetric Exact Solutions for Flagpole Fer…
We study a static, spherically symmetric system of (2j+1) massive Dirac particles, each having angular momentum j, j=1,2,..., in a classical gravitational and SU(2) Yang-Mills field. We show that for any black hole solution of the…
Solutions to the four-dimensional Euclidean Weyl equation in the background of a general JNR N-instanton are known to be normalisable and regular throughout four-space. We show that these solutions are asymptotically given by a linear…
This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4d. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in…
We show that, on a 4-manifold M endowed with a spin^c structure induced by an almost-complex structure, a self-dual (= positive) spinor field \phi \in \Gamma(W^+) is the same as a bundle morphism \phi: TM \to TM acting on the fiber by…
We study spin/fermion ladder models with exact multipole phases, which are traditional spin phases formed by multipole moments. These phases feature non-trivial order with zero magnetization. The multipole models have dimer local conserved…
We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating…
We study essentially non-Abelian backgrounds in the five dimensional N=4 gauged SU(2)$\times$U(1) supergravity. Static configurations that are invariant under either the SO(4) spatial rotations or with respect to the SO(3) rotations and…
The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations.…
Five-dimensional gauge and gravity theories are known to exhibit striking properties. D=5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor…
We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the…
The study of a self-consistent system of nonlinear spinor and Bianchi type I gravitational fields in presence of a viscous fluid and $\Lambda$ term with the spinor field nonlinearity being some arbitrary functions of the invariants $I$ an…
Using a theorem of Jackiw and Pi expressing the delicate balance of the spin and the orbital momentum, we systematically classify the flat-space massless Lagrangian quantum field theories that are invariant under the global conformal group…
After reviewing the Lounesto spinor field classification, according to the bilinear covariants associated to a spinor field, we call attention and unravel some prominent features involving unexpected properties about spinor fields under…
15 exactly solvable inhomogeneous (spinless) fermion systems on one-dimensional lattices are constructed explicitly based on the discrete orthogonal polynomials of Askey scheme, e.g. the Krawtchouk, Hahn, Racah, Meixner, $q$-Racah…
In this note, we characterise the existence of non-trivial invariant spinors on maximal flag manifolds associated to complex simple Lie algebras. This characterisation is based on the combinatorial properties of their set of positive roots.…
We show that Majorana particles belong to the Wigner class of fermions in which the charge conjugation and the parity operators commute, rather than anticommute. Rigorously speaking, Majorana spinors do not satisfy the Dirac equation [a…
Spin 1/2 fields localization on an asymmetric dS${}_4$ scenario, where the brane interpolates between two spacetimes dS${}_5$ and AdS${}_5$, is determined. The bulk spinor is coupled to scalar field of the brane by a nonminimal Yukawa term…
From the Killing spinor equation and the equations satisfied by their bilinears we deduce some well known bosonic and fermionic field equations of mathematical physics. Aside from the trivially satisfied Dirac equation, these relativistic…
We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the…
We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of…