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In particle physics, the doublet–triplet (splitting) problem is a problem of some Grand Unified Theories, such as SU(5), SO(10), and .Grand unified theories predict Higgs bosons (doublets of ()) arise from representations of the unified group that contain other states, in particular, states that are triplets of color.
In quantum mechanics, a doublet is a composite quantum state of a system with an effective spin of 1/2, such that there are two allowed values of the spin component, −1/2 and +1/2. Quantum systems with two possible states are sometimes called two-level systems .
The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total orbital angular momentum, which is also 1 as indicated by the letter P. The total angular momentum quantum number J can vary from L+S = 2 to L–S = 0 in integer steps, so that J = 2, 1 or 0.
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.
Many word processing and desktop publishing software products have built-in features to control line breaking rules in those languages. In the Japanese language, especially, the categories of line breaking rules and processing methods are determined by the Japanese Industrial Standard JIS X 4051 , and it is called Kinsoku Shori ( 禁則処理 ) .
Left: when 2 J-coupling constants are sufficiently unequal (Jab>Jbc) for spin ½ nuclei, a doublet of doublets with an intensity ratio of about 1:1:1:1 is seen in NMR spectra. Right: when Jab=Jbc for spin ½ nuclei, a triplet (collapsed or overlapping doublet of doublets) with an intensity ratio of about 1:2:1 is always seen in NMR spectra.
Examples of atoms in singlet, doublet, and triplet states. In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis m S = −1, 0, or +1, giving the name "triplet".
Name or phenomenon Description Diagram Beta decay: beta particle is emitted from an atomic nucleus : Compton scattering: scattering of a photon by a charged particle Neutrino-less double beta decay