Structural Properties of Irreducible Two-Particle Representations of the Poincaré Group

Two particles, described by an irreducible two-particle representation of the Poincaré group, are correlated by the constraints that the constancy of the Casimir operators imposes on the state space. This correlation can be understood as a geometrically caused interaction between the particles, the strength of which is related to the normalisation constant $\omega$ of the two-particle states by $4\pi {\omega }^2$. The numerical value of $4\pi {\omega }^2$ is found to match the experimental value of the electromagnetic fine structure constant $\alpha$. This strongly suggests that the correlation of two particles in an irreducible two-particle representation of the Poincaré group manifests itself in the electromagnetic interaction.