This entry is about the concept in supergeometry. For the concept in gravity/cosmology see at Wheeler superspace.
superalgebra and (synthetic ) supergeometry
Physicists often refer to spaces in supergeometry, such as supermanifolds or super schemes, as superspaces. Hence a superspace can be an affine superspace (the affine counterpart of the super vector space over real or complex numbers), superscheme, supermanifold, etc.
Mostly however “superspace” is used for superspacetimes, and here mostly for super Minkowski spacetimes.
The concept of superspace in physics (together with that of superfields) is due to
Abdus Salam, John Strathdee, Supergauge Transformations, Nucl.Phys. B76 (1974) 477-482 (spire:89208)
Abdus Salam, John Strathdee, Superfields and Fermi-Bose symmetry, Physical Review D11, 1521-1535 (1975) (doi:10.1142/9789812795915_0051)
(which considered superspace of dimension $d = 4$ with number of supersymmetries $N = 2$, hence the supermanifold $\mathbb{R}^{4\vert \mathbf{4}+ \mathbf{4}}$, or rather the super Minkowski spacetime $\mathbb{R}^{3,1\vert \mathbf{4}+ \mathbf{4}}$)
A textbook account is
Further review includes the following:
I. L. Buchbinder, S. M. Kuzenko, Ideas and methods of supersymmetry and supergravity; or A walk through superspace
Albert Schwarz, On the definition of superspace Teoret. Mat. Fiz., 1984, Volume 60, Number 1, Pages 37–42 (Mi tmf5111), (russian original)
Last revised on January 11, 2021 at 03:28:03. See the history of this page for a list of all contributions to it.