# Multiplet

## Representation theory

A multiplet is terminology, often used in physics, for the representation of a mathematical structure, usually an irreducible representation of a Lie group acting as linear operators on a real or complex vector space.

## Physics

### Quantum physics

In quantum physics, the mathematical notion is usually applied to representations of the gauge group. E.g. an SU(2) gauge theory will have "multiplets" which are fields whose representation of SU(2) is determined by the single half integer number s, the (iso)"spin" since irreducible SU(2) representations are isomorphic to the 2sth symmetric power of the fundamental representation, every field has 2s symmetrised "internal indices". Fields are also transforming under representations of the Lorentz group (e.g. in the vector representation) or its spin group SL(2, 'C') (e.g. as Weyl spinors), which give the fields "Lorentz or (confusingly) "spin indices", 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.

Multiplet may also describe a group of related spectral lines.[why?]

#### 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 a vector representation.

In QCD, quarks are in a multiplet of SU(3).

### Seismology

In seismology, multiplet refers to a repeating earthquake, occurring in nearly the same location, with nearly the same source characteristics.