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

Two particles, described by an irreducible two-particle representation of the Poincare 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 Poincare group manifests itself in the electromagnetic interaction.