Superspace
"Superspace" is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions x, y, z, ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom.
The word "superspace" was first used by John Wheeler in an unrelated sense to describe the configuration space of general relativity; for example, this usage may be seen in his 1973 textbook Gravitation.
There are several similar, but not equivalent, definitions of superspace that have been used, and continue to be used in the mathematical and physics literature. One such usage is as a synonym for super Minkowski space. In this case, one takes ordinary Minkowski space, and extends it with anti-commuting fermionic degrees of freedom, taken to be anti-commuting Weyl spinors from the Clifford algebra associated to the Lorentz group. Equivalently, the super Minkowski space can be understood as the quotient of the super Poincaré algebra modulo the algebra of the Lorentz group. A typical notation for the coordinates on such a space is with the overline being the give-away that super Minkowski space is the intended space.
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