Related papers: Wigner's Spins, Feynman's Partons, and Their Commo…
The concept of elementary particle rests on the idea that it is a physical system with no excited states, so that all possible states of the particle are just kinematical modifications of any one of them. In this way instead of describing…
It is noted that the Poincar\'e sphere for polarization optics contains the symmetries of the Lorentz group. The sphere is thus capable of describing the internal space-time symmetries dictated by Wigner's little groups. For massive…
Four $SL(2,C)$ spinors are considered within the framework of Wigner's little groups which dictate internal space-time symmetries of relativistic particles. It is indicated that the little group for a massive particle at rest is $O(3)$,…
It is known that two coupled harmonic oscillators can support the symmetry group as rich as O(3,3) which corresponds to the Lorentz group applicable to three space-like and three time-like coordinates. This group contains many subgroups,…
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…
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…
Extended particles are considered in terms of the fields on the Poincar\'{e} group. Dirac like wave equations for extended particles of any spin are defined on the various homogeneous spaces of the Poincar\'{e} group. Free fields of the…
We study the asymptotic behavior of a singular potential, and discuss the self-consistency condition for the spherical symmetric Klein-Gordon equation. In our view, gravity and the weak force are subsidiary, derived from electricity.…
It was shown that in the small Wigner group there is a one-parameter subgroup of the Lorentz transformations, which leave unchanged not only the momentum of the fermion with spin h/2, but also its spin characteristics. This is the group of…
Wigner's 1939 paper on representations of the inhomogeneous Lorentz group is one of the most fundamental papers in physics. Wigner maintained his passion for this subject throughout his life. In this report, I will review the papers which…
We consider Einstein gravity with positive cosmological constant coupled with higher spin interactions and calculate Euclidean path integral perturbatively. We confine ourselves to the static patch of the 3 dimensional de Sitter space. This…
Wigner's particle classification provides for "continuous spin" representations of the Poincar\'e group, corresponding to a class of (as yet unobserved) massless particles. Rather than building their induced realizations by use of "Wigner…
Since quarks are regarded as the most fundamental particles which constitute hadrons that we observe in the real world, there are many theories about how many of them are needed and what quantum numbers they carry. Another important…
Starting with the Chern-Simons formulation of (2+1)-dimensional gravity we show that the gravitational interactions deform the Poincare symmetry of flat space-time to a quantum group symmetry. The relevant quantum group is the quantum…
Searches for the role of spin in gravitation dated before the firm establishment of the electron spin in 1925. Since mass and spin, or helicity in the case of zero mass, are the Casimir invariants of the Poincar\'e group and mass…
When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is…
Henri Poincar\'e formulated the mathematics of Lorentz transformations, known as the Poincar\'e group. He also formulated the Poincar\'e sphere for polarization optics. It is shown that these two mathematical instruments can be derived from…
The E. Cartan's equations defining "simple" spinors (renamed "pure" by C. Chevalley) are interpreted as equations of motions for fermion multiplets in momentum spaces which, in a constructive approach based bilinearly on those spinors,…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting…