Related papers: Projectively-Compact Spinor Vertices and Space-Tim…

In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the…

The paper discusses stably trivial torsors for spin and orthogonal groups over smooth affine schemes over infinite perfect fields of characteristic unequal to 2. We give a complete description of all the invariants relevant for the…

Conformally compactified phase space is conceived as an automorphism space for the global action of the extended conformal group. Space time and momentum space appear then as conformally dual, that is conjugate with respect to conformal…

In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…

Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the…

The question of the interpretation of Wheeler-DeWitt solutions in the context of cosmological models is addressed by implementing the Hamiltonian constraint as a spinor wave equation in minisuperspace. We offer a relative probability…

This article gives a geometric interpretation of the spin base formulation with local spin base invariance of spinors on a curved space-time and in particular of a central element, the global Dirac structure, in terms of principal and…

Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…

Higher spin theories can be efficiently described in terms of auxiliary St\"uckelberg or projective space field multiplets. By considering how higher spin models couple to scale, these approaches can be unified in a conformal…

In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space $M_\Sigma$ with singular stratum $\beta M$ (a closed manifold of positive codimension) and associated link equal to…

Using the complete orthonormal sets of radial parts of nonrelativitistic exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical harmonics of rank s the new formulae for the 2(2s+1)-component relativistic spinors…

We investigate the implications of the existence of Killing spinors in a spacetime. In particular, we show that in vacuum and electrovacuum a Killing spinor, along with some assumptions on the associated Killing vector in an asymptotic…

We parametrize pp-wave spacetimes with compact codimension 2 hypersurfaces. In the vacuum case, we show that these spacetimes are locally in one-to-one correspondence with smooth curves of Riemannian Ricci-flat metrics modulo smooth curves…

Rigidity results for asymptotically locally hyperbolic manifolds with lower bounds on scalar curvature are proved using spinor methods related to the Witten proof of the positive mass theorem. The argument is based on a study of the Dirac…

Recently, the generating system that describes interacting symmetric higher-spin gauge fields at the level of equations of motion was proposed. The interaction vertices it offers are 'off the mass shell' unless constrained by the prescribed…

It is introduced the concept of a quasi-king space, which is a natural generalisation of a king space. In the realm of suborderable spaces, king spaces are precisely the compact spaces, so are the quasi-king spaces. In contrast, quasi-king…

A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…

An attempt is made of giving a self-contained (although incomplete) introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, two-component…

We recall some basic aspects of line and line Complex representations, of symplectic symmetry emerging in bilinear point transformations as well as of Lie transfer of lines to spheres. Here, we identify SU(2) spin in terms of (classical)…