Related papers: A Walk Through $Spin(1,d+1)$
In this paper, a gauge invariant description of massive higher spin bosonic and fermionic particles in frame-like Lagrangian and unfolded formalism in (A)dS${}_4$ is built. A complete set of gauge invariant object is also constructed and…
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…
Quantum groups in general and the quantum Anti-de Sitter group $U_q(so(2,3))$ in particular are studied from the point of view of quantum field theory. We show that if $q$ is a suitable root of unity, there exist finite-dimensional, unitary…
We consider dS_2/CFT_1 where the asymptotic symmetry group of the de Sitter spacetime contains the Virasoro algebra. We construct representations of the Virasoro algebra realized in the Fock space of a massive scalar field in de Sitter,…
Respecting the group theoretical approach, it is discussed that the linear conformal gravity can be written in terms of a mixed symmetry tensor field of rank-3 \cite{binegar}. Following this path, related field equation was obtained in de…
Arbitrary spin free massless fermionic fields corresponding to mixed symmetry representations of the \hbox{$SO(d-1)$} compact group and propagating in even $d$-dimensional anti-de Sitter spacetime are investigated. Free wave equations of…
We explicitly rewrite the path integral for the free or critical $O(N)$ (or $U(N)$) bosonic vector models in $d$ space-time dimensions as a path integral over fields (including massless high-spin fields) living on ($d+1$)-dimensional…
In this paper some properties of the irreducible multiplets of representation for the N = (p, q) - extended supersymmetry in one dimension are discussed. Essentially two results are here presented. At first a peculiar property of the one…
We consider unconstrained formulation of the higher spin gauge theory in anti de Sitter (AdS) spacetime, given by actions [1, 2], and provide on-shell supersymmetry transformations for the $\mathcal{N}=1$ unconstrained massless higher spin…
The fundamental fermion representations of causal spinor fields have previously been demonstrated to describe free Dirac fermions, as well as incorporate \emph{only} the observed degrees of freedom for local gauge invariance. In this paper,…
We study Discrete Series representations of $SL(2,\mathbb{R})$ with half-integer scaling dimension $\Delta$. At the classical level, we show that these UIRs are realised in the space of mode solutions of spinor fields with imaginary mass…
We explore analytical aspects of correlators involving Dirac spinors in $d+1$- dimensional de Sitter space. Adapting the formalism of Sleight and Taronna, we show how to relate processes involving fermions in the in-in formalism to…
Linear spinor fields are a generalization of the Dirac field that have direct correspondence with the known physics of fermions, inherent causality properties in their most fundamental constructions, and positive mass eigenvalues for all…
Fock module realization for the unitary singleton representations of the $d-1$ dimensional conformal algebra $o(d-1,2)$, which correspond to the spaces of one-particle states of massless scalar and spinor in $d-1$ dimensions, is given. The…
We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the…
We consider the consequences of global higher-spin symmetries in quantum field theories on a fixed de Sitter background of spacetime dimension $D \ge 3$. These symmetries enhance the symmetry group associated with the isometries of the de…
We construct, for spin $0,1,2$ tensor fields on S$^d$, a set of ladder operators that connect the distinct UIRs of SO$(d+1)$. This is achieved by relying on the conformal Killing vectors of S$^d$. For the case of spinning fields, the ladder…
The symmetry group of the de Sitter spacetime, accommodates fields of various masses and spin among its unitary irreducible representations. These unitary representations are labeled by the spin and the weight contribution to the scaling…
We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are…
In a space of $d=15 $ Grassmann coordinates, two types of generators of the Lorentz transformations, one of spinorial and the other of vectorial character, both linear operators in Grassmann space, forming the group $ SO(1,14) $ which…