singlets

A singlet (plural singlets) is a term used in various disciplines to describe an object that is invariant under a symmetry transformation or forms a one-dimensional representation of a symmetry group. In common usage, singlets are associated with total spin or charges that do not participate in certain interactions.

In particle physics, a gauge singlet is a field that carries no color, weak isospin, or hypercharge under the Standard Model gauge group SU(3)×SU(2)×U(1). Such fields interact only through renormalizable couplings or via mixing with other fields, and they appear in extensions of the Standard Model as, for example, singlet scalar fields or singlet fermions that may serve as dark matter candidates or influence Higgs phenomenology.

In quantum mechanics, a spin singlet state is the total spin S=0 configuration of two spin-1/2 particles. The state is antisymmetric with respect to particle exchange and yields opposite spins (one up, one down) in a correlated fashion. By contrast, the triplet states have S=1 and are symmetric in spin.

In chemistry and spectroscopy, a singlet state refers to an electronic configuration in which all electrons are paired with opposite spins, giving a net spin of zero. Singlet excited states can be accessed by allowed transitions, and they contrast with triplet states, which are often involved in phosphorescence and intersystem crossing.

In mathematics, a singlet (or trivial representation) is a one-dimensional irreducible representation of a group in which every group element maps to 1. Such representations appear in representation theory, where they are the simplest possible representations and often serve as a baseline for decomposing more complex representations.