Related papers: Linear Spinor Fields in Relativistic Dynamics
We consider the Dirac equations in static spherically-symmetric space-times, and we present a type of spinor field whose structure allows the separation of elevation angle and radial coordinate in very general situations. We demonstrate…
We give a streamlined account of $2$-spinors, up to and including the Dirac equation, using little more than the resources of linear algebra. We prove that the Dirac bundle is isomorphic to the associated bundles $\mathrm{SL}_2(\mathbb{C})…
A self-consistent system of nonlinear spinor and Bianchi type-V anisotropic gravitational fields are investigated. It is found that the presence of nontrivial non-diagonal components of the energy-momentum tensor of the spinor field imposes…
This paper shows how to obtain the spinor field and dynamics from the vielbein and geometry of General Relativity. The spinor field is physically realized as an orthogonal transformation of the vielbein, and the spinor action enters as the…
Operator fields in the bundle of Dirac spinors and their conversion to spatial fields are considered. Some commutator equations are studied with the use of the conversion technique.
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…
Spinor fields on surfaces of revolution conformally immersed into 3-dimensional space are considered in the framework of the spinor representations of surfaces. It is shown that a linear problem (a 2-dimensional Dirac equation) related with…
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…
The questions of the existence, basic algebraic properties and relevant constraints that yield a viable physical interpretation of world spinors are discussed in details. Relations between spinorial wave equations that transform…
A unified description of all interactions could be based on a higher-dimensional theory involving only spinor fields. The metric arises as a composite object and the gravitational field equations contain torsion-corrections as compared to…
The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional…
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…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
Inthispaper,weinvestigatethescatteringtheoryofhalf-spinwavesthroughtheuse of radiation fields. We define the radiation fields for semilinear Dirac equations with spinor null forms and establish a nonlinear isomorphism between the weighted…
The spin connections of the Dirac field have three ingredients that are connected with the Ricci rotations, the Maxwell field, and an axial field which is coupled to the axial current. I demonstrate that the axial field provides an…
Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator.…
Solutions of classical and quantum equations of motion in spinor electrodynamics are constructed within the context of perturbation theory. The solutions possess a graphical representation in terms of diagrams.
We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be $\lambda F$, with $\lambda$ being a self-coupling constant…
The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic `building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved…
A noncommutative-geometric generalization of the classical concept of spinor structure is presented. This is done in the framework of the formalism of quantum principal bundles. In particular, analogs of the Dirac operator and the Laplacian…