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arXiv · 2211.15452

Structural Properties of Irreducible Two-Particle Representations of the Poincar\'e Group

Walter Smilga
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Abstract

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

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Walter Smilga. 2022-11-22. Structural Properties of Irreducible Two-Particle Representations of the Poincar\'e Group. https://doi.org/10.1007/s10701-019-00277-9

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