Bound System of QED with Arbitrary Spin

Inspired by persistent discrepancies of theoretical predictions and experimental result for the hyperfine splitting in muonic deuterium, we explore Coulombic bound systems composed of particles of arbitrary spin. One example is deuteronium, the bound system of a deuteron (spin-one) and its antiparticle. The fine-structure of this system (arXiv:2506.15974) offers deep insights into the coupling of spin-one particles with the electromagnetic field. The relativistic, spin-dependent corrections to the bound-state energy levels are obtained from the Breit Hamiltonian, suitably generalized to arbitrary spin. Extreme electromagnetic field strengths, which exceed the Schwinger limit, are encountered in the bound system. Measurements of Rydberg states with nonvanishing angular momenta are sensitive probes of spin-one electromagnetic interactions. Furthermore, intrinsic properties of the constituent particles (scalar and tensor polarizabilities) contribute to the spectrum and could be studied in future experiments. Deuteronium and other, generalized "exotic" bound systems (composed of spin-one particles) offer unique possibilities to study relativistic, spin-dependent, and QED radiative (vacuum-polarization) effects in extreme environments. Any conceivable discrepancies of theory and experiment could indicate the presence of New Physics, or, they might alter our understanding of spin-dependent electromagnetic interactions, possibly contributing to the theory of the hyperfine splitting in muonic bound systems.