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| In [[theoretical physics]], one often analyzes theories with [[supersymmetry]] in which '''superfields''' play a very important role. A superfield is a function defined in [[superspace]] which properly packages the various fields of a [[supermultiplet]], namely, the array of [[fermion]] and [[boson]] fields related among themselves by [[supersymmetry]]. Superfields were introduced by [[Abdus Salam]] and John Strathdee in 1979.<ref>{{cite doi|10.1016/0550-3213(74)90537-9|noedit}}</ref>
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| ==Overview==
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| In four dimensions, the simplest example—namely, the minimal ''N = 1'' supersymmetry—may be written as a vector in a [[superspace]] with four extra fermionic coordinates <math>\theta^1,\theta^2,\bar\theta^1,\bar\theta^2</math>, transforming as a two-component [[spinor]] and its conjugate. More generally, there are 4N extra fermionic ([[Grassmann number]]) coordinates .
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| A more coordinate-free description of the superspace is that it's the [[quotient space]] of the [[super-Poincaré group]] divided by the [[Lorentz group]].
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| Every superfield, i.e. a field that depends on all coordinates of the superspace (or in other words, an element of a [[Module (mathematics)|module]] of the algebra of functions over superspace), may be expanded with respect to the new fermionic coordinates. There exists a special kind of superfields, the so-called ''chiral superfields'', that, in the chiral representation of supersymmetry, depend only on the variables ''θ'' but not their conjugates. The last term in the corresponding expansion, namely <math>F \theta^1\theta^2</math>, is called the ''F-term''. Other superfields include [[vector superfield]]s.
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| There also exist superfields in theories with larger supersymmetry.
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| Manifestly supersymmetric actions may also be written as [[integral]]s over the whole superspace. Some special terms, such as the [[superpotential]], may be written as integrals over ''θ''s only. They are also referred to as ''F''-terms, much like the terms in the ordinary potential that arise from these terms of the supersymmetric Lagrangian.
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| ==References==
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| {{Reflist|30em}}
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| {{quantum-stub}}
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| [[Category:Supersymmetry]]
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| [[Category:Quantum field theory]]
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| [[Category:Theoretical physics]]
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