theory In quantum physics, the mathematical notion is usually applied to representations of the gauge group. For example, an gauge theory will have multiplets which are fields whose representation of is determined by the single half-integer number , the isospin. Since irreducible representations are isomorphic to the th symmetric power of the fundamental representation, every field has symmetrized internal indices. Fields also transform under representations of the Lorentz group , or more generally its spin group which can be identified with due to an exceptional isomorphism. Examples include scalar fields, commonly denoted , which transform in the trivial representation, vector fields (strictly, this might be more accurately labelled a covector field), which transforms as a 4-vector, and spinor fields such as Dirac or Weyl spinors which transform in representations of . A right-handed Weyl spinor transforms in the fundamental representation, , of . Beware that besides the Lorentz group, a field can transform under the action of a gauge group. For example a scalar field , where is a spacetime point, might have an isospin state taking values in the fundamental representation of . Then is a vector valued function of spacetime, but is still referred to as a scalar field, as it transforms trivially under Lorentz transformations. In quantum field theory different particles correspond one to one with gauged fields transforming in irreducible representations of the internal and Lorentz group. Thus, a multiplet has also come to describe a collection of subatomic particles described by these representations. Examples The best known example is a spin multiplet, which describes symmetries of a group representation of an SU(2) subgroup of the Lorentz algebra, which is used to define spin quantization. A spin singlet is a trivial representation, a spin doublet is a fundamental representation and a spin triplet is in the vector representation or adjoint representation. In QCD, quarks are in a multiplet of SU(3), specifically the three-dimensional fundamental representation. Other uses Spectroscopy In spectroscopy, particularly Gamma spectroscopy and X-ray spectroscopy, a multiplet is a group of related or unresolvable spectral lines. Where the number of unresolved lines is small, these are often referred to specifically as doublet or triplet peaks, while multiplet is used to describe groups of peaks in any number. References Georgi, H. (1999). Lie Algebras in Particle Physics: From Isospin to Unified Theories (1st ed.). CRC Press. https://doi.org/10.1201/9780429499210 See also Hypercharge Isospin Spin (physics) Group representation Multiplicity