Speaker
Description
Wigner’s paradigm identifies elementary systems with unitary irreducible representations (UIRs) of spacetime symmetry groups. In constant-curvature spacetimes, however, the notion of masslessness is no longer intrinsic. This motivates the search for a framework in which massless systems can be characterized in a geometrically and representation-theoretically coherent way across flat, de Sitter ($dS$), and anti-de Sitter ($AdS$) settings.
In four spacetime dimensions, massless systems admit conformal extensions governed by $U(2,2)$, whose positive-energy ladder representations encode fields of arbitrary helicity. In this talk, we develop a concrete realization of these representations within the conformal Clifford algebra $cl(4,2)$, based on a canonical real (Majorana) spinor structure arising from the split-octonion algebra. This yields a unified algebraic setting in which Poincaré, $(A)dS$, and conformal symmetries are realized within the same framework, with spinorial carriers, symmetry generators, and group actions emerging from a common structure.
Within this setting, the ladder representations can be analyzed directly, together with their restrictions to the Poincaré and $(A)dS$ symmetry algebras, leading to a coherent description of massless systems of arbitrary helicity in flat and constant-curvature spacetimes.