Related papers: Spinors and essential dimension
We studied (arxiv: 1001.4679, 1205.1714) properties of spinors in a toy model in $d=(1+5)$ as a step towards realistic Kaluza-Klein (like) theories in non compact spaces. ${\cal M}^{(5+1)}$ was assumed to break to an infinite disc with a…
Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions $D$. This is achieved in terms of a mixed…
We studied properties of spinors in a toy model in $d=(5+1)$, when ${\cal M}^{(5+1)}$ breaks to an infinite disc with a zweibein which makes a disc curved on an almost $S^2$ and with a spin connection field which allows on such a sphere…
We emphasize that the group-theoretical considerations leading to SO(10) unification of electro-weak and strong matter field components naturally extend to space-time components, providing a truly unified description of all generation…
There are several approaches to formulate gauge-invariant models for massive integer-spin fields in $d$ dimensions including the following: (i) in terms of symmetric tensor fields $\phi_{\mu_1 \dots \mu_k} $, with $k = s, s-1, \dots , 0$,…
In this paper, we fill some gap in the existing literature on higher spins by presenting an explicit solution to the on-shell constraints for a frame-like, gauge invariant description of massive, higher spin fields in d=4. We begin with the…
Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also…
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…
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher…
For each integer $d$ at least two, we construct non-spin closed oriented flat manifolds with holonomy group $\mathbb Z_2^d$ and with the property that all of their finite proper covers have a spin structure. Moreover, all such covers have…
A self-contained review on spin-half mass dimension one fermions and their higher-spin generalizations is presented. Starting from the two-component left-handed Weyl spinors, the Dirac spinors and Elko (eigenspinors of the charge…
Invariants of $G_2$ and $Spin(7)$, both acting on several copies of octonions, have been decribed in \cite{schw2} over a ground field of characteristic zero. In the current manuscript, we extend this result to an arbitrary infinite field of…
Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,...,11 are calculated for all massless, and partially for massive orbits. For massless orbits little…
I outline a series of results obtained in collaboration with A. Waldron on the properties of massive higher (s>1) spin fields in cosmological, constant curvature, backgrounds and the resulting unexpected qualitative effects on their degrees…
By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex…
This review is devoted to highlight some aspects of the relevance of Majorana fermions in rigid supersymmetry breaking in four spacetime dimensions. After introducing some basic facts on spinors, and on their symmetries and reality…
We define spin structures on perfect complexes outside of characteristic two, generalizing the usual notion for vector bundles. We give an explicit local characterization of spin structures, and show that for an oriented quadratic complex…
General relativity and quantum field theory are the cornerstones of our understanding of physical processes, from subatomic to cosmic scales. While both theories work remarkably well in their tested domains, they show minimal overlap.…
There are two well-known ways of describing elements of the rotation group SO$(m)$. First, according to the Cartan-Dieudonn\'e theorem, every rotation matrix can be written as an even number of reflections. And second, they can also be…
We construct, in D=3,4,6 and 10 space-time dimensions, supersymmetric Lagrangians for free massless higher spin fields which belong to reducible representations of the Poincare group.The fermionic part of these models consists of…