Related papers: Massless and massive representations in the spinor…
Here we perform a Kaluza-Klein dimensional reduction of Vasiliev's first-order description of massless spin-s particles from $D=3+1$ to $D=2+1$ and derive first-order self-dual models describing particles with helicities $\pm s$ for the…
We study algebraic varieties that encode the kinematic data for $n$ massless particles in $d$-dimensional spacetime subject to momentum conservation. Their coordinates are spinor brackets, which we derive from the Clifford algebra…
Polynomials in Grassmann space can be used to describe all the internal degrees of freedom of spinors, scalars and vectors, that is their spins and charges. It was shown that K\"ahler spinors, which are polynomials of differential forms,…
The genuine Kaluza-Klein-like theories (with no fields in addition to gravity) have difficulties with the existence of massless spinors after the ompactification of some of dimensions of space\cite{witten}. We assume a $M^{(1+3)} \times$ a…
A pseudoclassical model, reproducing, upon quantization, the dynamics of the chiral sectors of the massless spin-1/2 field theory is proposed. The discrete symmetries of the action are studied in details. In order to reproduce the positive…
We consider the representations of the optical Dirac equation, especially ones where the Hamiltonian is purely real-valued. This is equivalent, for Maxwell's equations, to the Majorana representation of the massless Dirac (Weyl) equation.…
We give a brief overview of some three-dimensional toy models for higher-spin interactions. We first review the construction of pure higher-spin gauge theories in terms of Chern-Simons theories. We then discuss how this setup could be…
Relativistic particles with spins $J>0$ are described by means of multicomponent wave functions which transform covariantly according to Lorentz-group representations that contain at rest the spin of interest. The symmetry group of…
In a previous paper, we considered the motion of massive spinning test particles in the "pole-dipole" approximation, as described by the Mathisson--Papapetrou--Dixon (MPD) equations, and examined its properties in dependence on the spin…
An explicit construction of theories of spinning particles, both massive and massless, is given with arbitrary extended supersymmetry on the world-line. As an application of our results, we give a universal description of 3D (and via…
The stability of proton and neutrino masses are discussed in the Randall-Sundrum model. We show that relevant operators should be suppressed, if the hierarchical Yukawa matrices are explained only by configurations of wavefunctions for…
We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds.…
In the search of a mathematical basis for quantum mechanics, in order to render it self-consistent and rationally understandable, we find that the best approach is to adopt E. Cartan's way for discovering spinors; that is to start from…
We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space $\Delta \textstyle{\bigotimes \bigotimes^k V}$. Here $\Delta$ is the fundamental representation of…
In our previous article [Letsios 2023 J. High Energ. Phys. JHEP05(2023)015], we showed that the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields, on $N$-dimensional ($N \geq 3 $) de Sitter…
The first time that the connection between isometric immersion of surfaces and solutions of the Dirac equation appeared in the literature was in the seminal paper of Thomas Friedrich in 1998. In consequence of that, several authors…
The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…
The representation theory of the symmetric groups S_n is intimately related to combinatorics: combinatorial objects such as Young tableaux and combinatorial algorithms such as Murnaghan-Nakayama rule. In the limit as n tends to infinity,…
We analyze the possibility of description of D-dimensional massless particles by the Lagrangians linear on world-line curvatures k_i, {\cal S}=\sum_{i=1}^Nc_i\int k_i d{\tilde s}. We show, that the nontrivial classical solutions of this…
We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of…