Related papers: A space-time calculus based on symmetric 2-spinors
This paper studies spinor two-point functions for spin-1/2 and spin-3/2 fields in maximally symmetric spaces such as de Sitter spacetime, by using intrinsic geometric objects. The Feynman, positive- and negative-frequency Green functions…
The necessary and sufficient condition for the existence of $\alpha$-surfaces in complex space-time manifolds with nonvanishing torsion is derived. For these manifolds, Lie brackets of vector fields and spinor Ricci identities contain…
Superconformal algebras embedding space-time in any dimension and signature are considered. Different real forms of the $R$-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than…
We explicitly compute the Green's function of the spinor Klein-Gordon equation on the Riemannian and Lorentzian manifolds of the form $M_0 \times ... \times M_N$, with each factor being a space of constant sectional curvature. Our approach…
The exterior algebra of Minkowski space naturally has the structure of a sixteen-dimensional Clifford algebra representation, and so can be used as the space of spinors. We examine plane, circular, and spherical solutions to the free Dirac…
It is shown how the old Cartan's conjecture on the fundamental role of the geometry of simple (or pure) spinors, as bilinearly underlying euclidean geometry, may be extended also to quantum mechanics of fermions (in first quantization),…
It is shown that cosmological spacetime manifold has the structure of a Lie group and a spinor space. This leads naturally to the Minkowski metric on tangent spaces and the Lorentzian metric on the manifold and makes it possible to dispense…
In the existing implementations of the Cartan-Karlhede procedure for characterization and classification of spacetimes, a prominent r\^ole is played by multi-index two-component spinors symmetrized over both types of index. This paper…
A special approach to examine spinor structure of 3-space is proposed. It is based on the use of the concept of a spatial spinor defined through taking the square root of a real-valued 3-vector. Two sorts of spatial spinor according to…
We show how the space spinor formalism for 2-component spinors can be used to construct estimates for spinor fields satisfying first order equations. We discuss the connection of the approach presented in this article with other strategies…
We examine the structure of the Clifford algebra associated with a Hermitian bilinear form and apply the result to a dynamical model of the relativistic point particle. The dynamics of the particle is described by a Dirac spinor with…
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
Coupling spinor fields to the gravitational field, in the setting of general relativity, is standardly done via the introduction of a vierbein field and the (associated minimal) spin connection field. This makes three types of indices…
Within the scope of a static cylindrically symmetric space-time we study the behavior of a nonlinear spinor field that depends on time and radial coordinates. It is found that the presence of nontrivial non-diagonal components of the…
There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alignment theory, bivectors and discriminants. Previous work gave a set of necessary conditions in terms of discriminants for a spacetime to be of…
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 aim of this work is to find exact solutions of the Dirac equation in 1+1 space-time beyond the already known class. We consider exact spin (and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus (and…
We consider spinor representations of the conformal group. The spacetime is constructed by the 15-dimensional vectors in the adjoint representation of $SO(2,4)$. On the spacetime, we construct a gravitational model that is invariant under…
We review the relation between the "embedding" formalism and spinorial projective space. The latter is more convenient when treating spin (and indispensable for supersymmetry), as it maintains manifest conformal symmetry while using…
We consider quantum mechanical systems of spin chain type, with finite-dimensional Hilbert spaces and $\mathcal{N}=2$ or $\mathcal{N}=4$ supersymmetry, described in $\mathcal{N}=2$ superspace in terms of nonlinear chiral multiplets. We…