Spin-orbit duality

TL;DR

This paper introduces a novel duality in four-dimensional flat spacetime that exchanges spin and orbital angular momentum, revealing a holographic, noncommutative structure and suggesting spacetime quantization at a fundamental level.

Contribution

It proposes a new spin-orbit duality based on Hodge decomposition, connecting spacelike regions and holography, with implications for spacetime quantization.

Findings

Duality exchanges spin and orbital angular momentum.

Dual theory is noncommutative and defined by Poincaré Casimirs.

Spacetime may be fundamentally quantized for massive fields.

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.