multiplets

A multiplet is a set of states, particles, or spectral lines that are related by a symmetry of the underlying system and thus transform together under a symmetry group. In quantum mechanics, a multiplet forms the states that carry an irreducible representation of the symmetry group; members of the same multiplet are often degenerate in the symmetry limit and may become split when the symmetry is broken.

In particle and nuclear physics, approximate symmetries such as isospin (SU(2)) or flavor SU(3) organize particles into multiplets. For example, the proton and neutron constitute an isospin doublet, while broader organizations yield the baryon octet and decuplet and the meson nonet. These groupings reflect underlying similarities in composition and interactions, with observed splittings arising from mass differences, electromagnetic effects, or explicit symmetry-breaking terms.

In atomic and molecular spectroscopy, a multiplet can refer to a group of energy levels or spectral lines that share the same electronic configuration and total quantum numbers (as in LS coupling, where levels with a common term symbol are grouped into a multiplet). Spectral multiplets help explain patterns in spectra and the selection rules governing transitions. External perturbations such as magnetic or electric fields can lift degeneracies and split a multiplet into submultiplets (for example via the Zeeman or Stark effects).

More generally, in representation theory, a multiplet corresponds to the basis states of one irreducible representation of a symmetry group. Recognizing multiplets aids in understanding regularities in both spectra and particle classifications, providing a compact way to describe complex systems.