Related papers: Elementary Particles and Spin Representations

The fermionic fields of one generation of the Standard Model, including the Lorentz spinor degrees of freedom, can be identified with components of a single real 64-dimensional semi-spinor representation S of the group Spin(11,3). We…

We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin $s={3}/{2}, {5}/{2}$ with any mass parameter on $D$-dimensional ($D \geq 3$) de Sitter space ($dS_{D}$) and Unitary…

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…

We propose and develop a new method to classify orbits of the spin group ${\rm Spin}(2d)$ in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents, imposing the…

We investigate classical spin systems in $d\geq 1$ dimensions whose transfer operator commutes with the action of a nonamenable unitary representation of a symmetry group, here ${\rm SO}(1,N)$; these systems may alternatively be interpreted…

Those fundamental physical properties, such as phase transitions, Weyl fermions, and spin excitation, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups. Recently, it has come…

We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…

We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that…

We show how to obtain a single chiral family of an SO(10) GUT, starting from a Majorana-Weyl representation of a unifying ("GraviGUT") group SO(3,11), which contains the gravitational Lorentz group SO(3,1). An action is proposed, which…

As argued in our previous papers, it would be more natural to modify the standard approach to quantum theory by requiring that i) one unitary irreducible representation (UIR) of the symmetry algebra should describe a particle and its…

When developing a quantum theory for a physical system, one determines the system's symmetry group and its irreducible unitary representations. For Minkowski space, the symmetry group is the Poincar\'e group, $\mathbb{R}^4 \rtimes…

It is shown that electrons and photons can be considered as composities of particles representating the fundamental representation of the extended Lorentz group $SU(3)\otimes SU(3)$ in (8+1) dimensional space-time which are held together by…

We consider a Dirac equation set on an extended spin space that contains fermion and boson solutions. At given dimension, it determines the scalar symmetries. The standard field equations can be equivalently written in terms of such degrees…

A 5D SU(7) family unification model with two spinor representations of SO(14) is presented. The fifth dimension is compactified on $S^1/Z_2\times Z_2'$. The orbifolding is used to obtain 4D SO(10) chiral fermions. The 4D grand unification…

We construct an $SO(10)$ grand unified theory in the formulation of non-com-\break mutative geometry. The geometry of space-time is that of a product of a continuos four dimensional manifold times a discrete set of points. The properties of…

We study the mass scales in the $SO(10)$ grand unified theory based on the following minimal Higgs representation content: adjoint $45_{\rm H}$, spinor $16_{\rm H}$ and complex vector $10_{\rm H}$, with higher dimensional operators on top…

We know that any element A of the group SO(3) can be represented as A = A1 A2 A1', where A1, A1' are elements of SO1(2)={A is an element of SO(3) | Ae1=e1}, and SO2(2)={A is an element of SO(3) | Ae2=e2} . This fact is known as Euler's…

Spin-one matter fields are relevant both for the description of hadronic states and as potential extensions of the Standard Model. In this work we present a formalism for the description of massive spin-one fields transforming in the…

SO(10) grand unified theory seems to have all the ingredients to be a complete unified theory of quarks and leptons. I review here its minimal, possibly realistic versions, both supersymmetric and not.

A unified description of spacetime and matter is proposed by using a single irreducible representation of SO(10) Super-Poincare algebra(SO(10)SPA). All (observed) elementary particles except the graviton are the (massless) eigenstates of…