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 with number of supersymmetries , hence the supermanifold , or rather the super Minkowski spacetime )
Monographs:
Jim Gates Jr, Marcus Grisaru, Martin Roček, Warren Siegel, Superspace, or One thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1-548 [arXiv:hep-th/0108200, inspire:195126]
Ioseph L. Buchbinder, Sergei M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity – or: A Walk Through Superspace, IoP (1995) [doi:10.1201/9780367802530, inspire:1946734]
The formulation of supergravity on super spacetime supermanifolds:
Julius Wess, Bruno Zumino, Superspace formulation of supergravity, Phys. Lett. B 66 (1977) 361-364 [doi:10.1016/0370-2693(77)90015-6]
Richard Grimm, Julius Wess, Bruno Zumino, A complete solution of the Bianchi identities in superspace with supergravity constraints, Nuclear Phys. B 152 (1979) 255-265 [doi:10.1016/0550-3213(79)90102-0]
Warren Siegel, S. James Gates Jr., Superfield supergravity, Nuclear Physics B 147 1–2 (1979) 77-104 [doi:10.1016/0550-3213(79)90416-4]
S. James Gates Jr., Kellogg S. Stelle, Peter C. West Algebraic origins of superspace constraints in supergravity, Nuclear Physics B 169 3–4 (1980) 347-364 [doi:10.1016/0550-3213(80)90037-1]
Paul Howe, Supergravity in superspace, Nuclear Physics B 199 2 (1982) 309-364 [doi:10.1016/0550-3213(82)90349-2]
S. James Gates Jr., On-shell and conformal supergravity in superspace, Nuclear Physics B 213 3 (1983) 409-444 [doi:10.1016/0550-3213(83)90229-8]
For more on this see the:
See also:
S. M. Kuzenko, E. S. N. Raptakis, G. Tartaglino-Mazzucchelli, Superspace approaches to supergravity, Handbook of Quantum Gravity, Springer (2023) [arXiv:2210.17088]
S. M. Kuzenko, E. S. N. Raptakis, G. Tartaglino-Mazzucchelli, Covariant superspace approaches to supergravity, in: Handbook of Quantum Gravity, Springer (2023) [arXiv:2211.11162]
Further review:
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)
Discussion of superspace within philosophy of physics:
Last revised on March 17, 2024 at 16:41:02. See the history of this page for a list of all contributions to it.