Related papers: Let the spin and the charges unify
A representation of the Lorentz group is given in terms of 4 X 4 matrices defined over a simple non-division algebra. The transformation properties of the corresponding four component spinor are studied, and shown to be equivalent to the…
A left-invariant sub-Riemannian metric $d$ on the shortened Lorentz group $SO_0(2,1)$ under the condition that $d$ is right-invariant relative to the orthogonal Lie subgroup $1\otimes SO(2)$ is studied. The distance between arbitrary two…
To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian Gr(2,4) and four lattices of rank two. Here, the first two lattices originate from the plane and its orthogonal complement…
We generalize a family of Lagrangians with values in the Poincar\'e group ISO(d-1,1), which contain the description of spinning strings in flat (d-1)+1 dimensions, by including symmetric terms in the world-sheet coordinates. Then, by…
We construct a novel higher-spin theory of gravity in 2+1 spacetime dimensions. The construction is based on a higher-spin super-algebra extending the Poincare group. Our algebra accommodates all integer and half-integer spins from 1 to…
By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\Lambda$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of…
Models with gauge-Higgs unification on a flat space are typically affected by common problems, the main of which are the prediction of a too small top and Higgs mass and a too low compactification scale. We show how, by breaking the SO(4,1)…
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…
The group $SL(2,\mathbb{C})$ of all complex $2\times 2$ matrices with determinant one is closely related to the group $\boldsymbol{\mathcal{L}}_{+}^\uparrow$ of real $4\times 4$ matrices representing the restricted Lorentz transformations.…
The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincar\'e group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless…
This paper, which is meant to be a tribute to Minkowski's geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are displayed by the spacetime manifold in the…
In this paper delivered by Murray Gell-Mann at the Stony Brook Supergravity Workshop in 1979, several paths to unification are discussed, from N=8 supergravity to $SU_5$, $SO_{10}$, and $E_6$. Generalizations of $SO_{10}$ to spinor…
The coherent states associated to the discrete serie representations $D(E_o,s)$ of $SO(3,2)$ are constructed in terms of (spin-)tensor fields on $D=4$ anti-de Sitter space. For $E_o>s+5$ the linear space ${\cal H}_{E_o,s}$ spanned by these…
Positive energy ray representations of the Poincar\'e group are naturally subdivided into three classes according to their mass and spin content: m>0, m=0 finite helicity and m=0 infinite helicity. For a long time the localization…
We consider a $SO(d)$ gauge theory in an Euclidean $d$-dimensional space-time, which is known to be renormalizable to all orders in perturbation theory for $2\le{d}\le4$. Then, with the help of a space-time representation of the gauge…
In this work, we systematically derive explicit expressions for the Poincar\'e Group generators on arbitrary-rank tensors and spinor-tensors in $D=3+1$ and $D=2+1$ spacetimes, thus generalizing previous works in the literature for the…
We construct the manifestly Lorenz-invariant formulation of the N=1 D=4 massive superparticle with tensorial central charges. The model contains a real parameter k and at $k\ne 0$ possesses one $\kappa$-symmetry while at k=0 the number of…
We construct the manifestly Lorentz-invariant twistorial formulation of N=1 D=4 superparticle with tensorial central charges which describes massive and massless cases in a uniform manner. The tensorial central charges are realized in terms…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, particularly in ray optics and polarization optics. The beam…