Related papers: Continuous Spin Representations from Group Contrac…
Hypercubic groups in any dimension are defined and their conjugate classifications and representation theories are derived. Double group and spinor representation are introduced. A detailed calculation is carried out on the structures of…
A canonical realization of the BMS (Bondi-Metzner-Sachs) algebra is given on the phase space of the classical real Klein-Gordon field . By assuming the finiteness of the generators of the Poincar\'e group, it is shown that a countable set…
The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with…
We construct a new model of a particle propagating in $4D$, ${\cal N}=1$ superspace that describes the dynamics of a continuous spin irreducible representation of the Poincar\'{e} supergroup. The model is characterized by two-component Weyl…
We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1]. We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie…
We generalize to arbitrary dimension the construction of a covariant and supersymmetric constraint for the massless superPoincare algebra, which was given for the eleven-dimensional case in a previous work. We also contrast it with a…
The nonlinearity of the conformal group is an essential factor that ruins the global conformal invariance for interacting material fields. In this paper we attempt to track such nonlinearity from spacetime transformations to spinor…
We consider the operation of contraction of unitary irreducible representations of the de Sitter group $ SO(4,1) $. It is shown that a direct sum of unitary irreducible representations of the Poincar\'{e} group with different signs of the…
The original Bondi$-$Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian 4-dim space$-$times. As such, B is the best candidate for the universal symmetry group of General Relativity…
In this work we provide an elementary derivation of the indefinite spin groups in low-dimensions. Our approach relies on the isomorphism of Cl(p+1, q+1) to the algebra 2x2 matrices with entries in Cl(p,q), simple properties of Kronecker…
Manifestly covariant formulation of discrete-spin, real-mass unitary representations of the Poincar\'e group is given. We begin with a field of spin-frames associated with 4-mometa p and use them to simplify the eigenvalue problem for the…
All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…
The Poincar\'e sector of a recently deformed conformal algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, the symmetries of a new relativistic theory with two observer-independent…
Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum…
We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures…
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…
The geometrization of the Electro-Weak Model is achieved in a 5-dimensional Riemann-Cartan framework. Matter spinorial fields are extended to 5 dimensions by the choice of a proper dependence on the extra-coordinate and of a normalization…
World spinors are objects that transform w.r.t. double covering group $\bar{Diff}(4,R)$ of the Group of General Coordinate Transformations. The basic mathematical results and the corresponding physical interpretation concerning these,…
Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these…
In this paper, we use a version of the BF formulation of two-dimensional dilaton gravity that allows to define a gauge theory of the two-dimensional Poincar\'e or Maxwell algebras and several of their higher-spin generalisations, both of…