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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.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
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The free field model can be solved exactly, and then the solutions to the full model can be expressed as perturbations of the free field solutions, for example using the Dyson series. It should be observed that the decomposition into free fields and interactions is in principle arbitrary.
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.
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".
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