Spin-orbit duality

Abstract

A new duality is proposed in four-dimensional flat space, which exchanges between spin and orbital degrees of freedom. This is motivated by a Hodge decomposition of the angular-momentum bivector for massive fields, along which spin and orbital angular momentum are Hodge duals of one another. The duality respects Poincar\`e symmetry and is shown to transform between complementary spacelike regions, projecting a fixed three-dimensional de Sitter world-tube (around the center of mass) into the bulk of four-dimensional spacetime and vice versa. This state of affairs is interpreted as a realization of the holographic principle. The dual theory living on that tube turns out to be noncommutative and entirely defined by the Casimir elements of the Poincar\`e algebra. In fact, the mass is now an ultraviolet cutoff. This naturally suggests that, for a Poincar\`e or just Lorentz-invariant quantum theory with massive fields of nonzero spin, spacetime is quantized at the fundamental level.