Supergauge multiplets and superfields

Superfields are defined as functions of the space-time variable x and of anticommuting two-component spinors θ and overlineθ. They have definite transformation properties under supergauge transformations. Their expansion in θ and overlineθ generates a finite number of ordinary fields forming a multiplet. A number of operations are defined which allow the construction of new superfields from given ones. The corresponding set of multiplets is complete, in the sense that the product of any two can be decomposed as a sum of multiplets belonging to the same set.