Singlet

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A singlet is also the name of the attire worn by competitors in the sport of wrestling. Singlets are sleeveless and legged one-piece garments that are usually made from spandex that gives great support and takes sweat and moisture away from the skin. Singlet is also the predominant term used in Australian English and New Zealand English for tank top. For the British cipher machine codenamed Singlet, see BID/60.

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).