Related papers: "Minimal geometric data" approach to Dirac algebra…
The algebra of the generators for infinitesimal transformations of the $\Gamma={1 \over 2}$ representation of causal spinor fields (Dirac fields) \emph{explicitly} constructs the Minkowski metric \emph{within} the internal group space as a…
Minimal coupling of a Dirac field to gravity with the most general non-propagating torsion is considered in (1+2)-dimensions. The field equations are obtained from a lagrangian by a variational principle. The space-time torsion is…
A classification of spinor fields according to the associated bilinear covariants is constructed in arbitrary dimensions and metric signatures, generalizing Lounesto's 4D spinor field classification. In such a generalized classification a…
We introduce a functional that couples the nonlinear sigma model with a spinor field: $L=\int_M[|d\phi|^2+(\psi,\D\psi)]$. In two dimensions, it is conformally invariant. The critical points of this functional are called Dirac-harmonic…
Recent interest in point and line node semimetals has led to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific…
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the…
Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…
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…
In this review, basic definitions of spin geometry are given and some of its applications to supersymmetry, supergravity and condensed matter physics are summarized. Clifford algebras and spinors are defined and the first-order differential…
We give explicit bijective correspondences between three families of objects: certain pairs of quaternions, which we regard as spinors; certain flags in (1+4)-dimensional Minkowski space; and horospheres in 4-dimensional hyperbolic space…
This brief set of notes presents a modest introduction to the basic features entering the construction of supersymmetric quantum field theories in four-dimensional Minkowski spacetime, building a bridge from similar lectures presented at a…
We develop a conformally invariant (CI) framework in $(1+3)$-dimensional de Sitter (dS) spacetime, that unifies the descriptions of graviton, ``partially massless'' graviton, and photon fields. This framework is grounded in a rigorous…
We reduce the classification of all supersymmetric backgrounds in eleven dimensions to the evaluation of the supercovariant derivative and of an integrability condition, which contains the field equations, on six types of spinors. We…
We investigate the superalgebra of derivations generated by the fundamental forms on manifolds with reduced structure group. In particular, we point out a relation between the algebra of derivations of heterotic geometries that admit…
This is a guided tour through some selected topics in geometric analysis. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
Linear spinor fields are a generalization of the Dirac field that have transparent cluster decomposability properties needed for classical correspondence of relativistic quantum systems. The algebra of these fields directly incorporate…
Killing spinor identities relate components of equations of motion to each other for supersymmetric backgrounds. The only input required is the field content and the supersymmetry transformations of the fields, as long as an on-shell…
We present a second-quantized field theory of massive spin one-half particles or antiparticles in the presence of a weak gravitational field treated as a spin two external field in a flat Minkowski background. We solve the difficulties…