Related papers: Local Existence of Spinor- and Tensor Potentials
The ${\cal PT}$ symmetric version of the generalised Ginocchio potential, a member of the general exactly solvable Natanzon potential class is analysed and its properties are compared with those of ${\cal PT}$ symmetric potentials from the…
The Helmholtz equation for symmetric, traceless, second-rank tensor fields in three-dimensional flat space is solved in spherical and cylindrical coordinates by separation of variables making use of the corresponding spin-weighted…
As a means of examining the section condition and its possible solutions and relaxations, we perform twistor transforms related to versions of exceptional field theory with Minkowski signature. The spinor parametrisation of the momenta…
Four $SL(2,C)$ spinors are considered within the framework of Wigner's little groups which dictate internal space-time symmetries of relativistic particles. It is indicated that the little group for a massive particle at rest is $O(3)$,…
The exact solution of a system of bilinear identities derived in the first part of our work [Nucl.Phys.A 938 (2015) 59] for the case of real Grassmann-odd tensor aggregate of the type $(S,V_{\mu},\!\,^{\ast}T_{\mu \nu},A_{\mu}, P)$ is…
This paper studies necessary conditions for the existence of alpha-surfaces in complex space-time manifolds with nonvanishing torsion. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain explicitly the…
The transverse traceless spin-two tensor harmonics on $S^3$ and $H^3$ may be denoted by $T^{(kl)}{}_{ab}$. The index $k$ labels the (degenerate) eigenvalues of the Laplacian $\square$ and $l$ the other indices. We compute the bitensor…
We present new infinitesimal `conformal-like' symmetries for the field equations of strictly massless spin-$s \geq 3/2$ totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime ($dS_{4}$). The…
We study different aspects of the connections between local theory of Banach spaces and the problem of the extension of bilinear forms from subspaces of Banach spaces. Among other results, we prove that if $X$ is not a Hilbert space then…
In a previous paper [1] we proposed a purely mathematical way to quantum mechanics based on Cartan's simple spinors in their most elementary form of 2 component spinors. Here we proceed along that path proposing, this time, a symmetric…
Taking Euclidean signature space-time with its local Spin(4)=SU(2)xSU(2) group of space-time symmetries as fundamental, one can consistently gauge one SU(2) factor to get a chiral spin connection formulation of general relativity, the other…
We show that Poincar\'e invariance directly implies the existence of a complexified Minkowski space whose real and imaginary directions unify spacetime and spin, which we dub spinspacetime. Despite the intrinsic noncommutativity of spin,…
We present a comprehensive table of recurrence and differential relations obeyed by spin one-half spherical spinors (spinor spherical harmonics) $\Omega_{\kappa\mu}(\mathbf{n})$ used in relativistic atomic, molecular, and solid state…
In this paper, the pinching problems of complete $\lambda$-hypersurfaces in a Euclidean space $\mathbb R^{n+1}$ are studied. By making use of the Sobolev inequality, we prove a global pinching theorem of complete $\lambda$-hypersurfaces in…
Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…
The thick brane model supported by a nonlinear spinor field is constructed. The different cases with the various values of the cosmological constant $\Lambda (< = >) 0$ are investigated. It is shown that regular analytical spinor thick…
Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence…
In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor $\mathfrak{C}_{\alpha(n)}(h)$ is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential…
We introduce and carefully define an entire class of field theories based on non-standard spinors. Their dominant interaction is via the gravitational field which makes them naturally dark; we refer to them as Dark Spinors. We provide a…
One-dimensional potentials defined by $V^{(S)}(x) =S(S+1) \hbar^2 \pi^2 /[2ma^2\sin^2(\pi x/a)]$ (for integer $S$) arise in the repeated supersymmetrization of the infinite square well, here defined over the region $(0,a)$. We review the…