Singlet

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A singlet is the standard noun used to describe a sleeveless athletic jersey usually worn by runners or marathonists.

In theoretical physics, a singlet usually refers to a one-dimensional representation (e.g. a particle with vanishing spin). It may also refer to two or more particles prepared in a correlated state, such that the total angular momentum of the state is zero.

Singlets frequently occur in atomic physics as one of the two ways in which the spin of two electrons can be combined; the other being a triplet. A single electron has spin 1/2, and transforms as a doublet, that is, as the fundamental representation of the rotation group SU(2). The product of two doublet representations can be decomposed into the sum of the adjoint representation (the triplet) and the trivial representation, the singlet. More prosaically, a pair of electron spins can be combined to form a state of total spin 1 and a state of spin 0.

The singlet state formed from a pair of electrons has many peculiar properties, and plays a fundamental role in the EPR paradox and quantum entanglement. In Dirac notation this EPR state is usually represented as:

$\frac{1}{\sqrt{2}}\Big( |\uparrow \downarrow \rangle - |\downarrow \uparrow \rangle\Big)$

In chemistry, a singlet is a spectroscopic entity (usually NMR, or EPR) which appears as a single peak; usually these are associated with paired, uncoupled spin-states (spin = 0).

In optics, a singlet is a single lens (optics) element conforming to one of the six basic types. Singlets are the building blocks of lens systems.