Researchers have developed an invertible map connecting three-dimensional pressure and shear force distributions in the Breit frame with corresponding two-dimensional densities in the infinite-momentum frame for spin-1 hadrons. This advance is crucial for understanding the internal mechanical structure of these subatomic particles, offering a new perspective on how forces are distributed within them. The correspondence is achieved by combining geometric Abel transformations (forward and inverse) with recoil operators, after isolating Wigner rotation-induced mixing effects in the infinite-momentum frame.

Unlike spin-1/2 hadrons, spin-1 hadrons present additional complications due to the introduction of multipole structures in spatial relations. However, the researchers have shown that these structures do not introduce new mechanical information, as pre-existing constraints among form factors propagate into mechanical densities. This means that, despite the increased complexity, the mapping provides a coherent and complete description of the internal mechanical properties of spin-1 hadrons.

This work significantly contributes to the field of particle physics, providing a robust theoretical tool for interpreting experimental data and advancing our understanding of the structure of protons and other composite particles. The ability to relate distributions in different reference frames is fundamental for constructing more precise models of hadron internal dynamics and for exploring the implications of quantum chromodynamics (QCD) in describing matter at fundamental scales.