superalgebra and (synthetic ) supergeometry
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
The super Poincaré group is the Lie integration in supergeometry of the super Poincaré Lie algebra. This is a super Lie group-extension of the ordinary Poincaré group.
In physics an action/symmetry of the super Poincaré group is also called a supersymmetry.
The coset (super Klein geometry) of a super Poincaré group by the Spin group/Pin group inside it is a super translation group, whose underlying supermanifold is a super Minkowski spacetime.
Pierre Deligne, Daniel Freed, section 1.1 of Supersolutions (arXiv:hep-th/9901094)
in Pierre Deligne, Pavel Etingof, Dan Freed, L. Jeffrey, David Kazhdan, John Morgan, D.R. Morrison and Edward Witten, (eds.), Quantum Fields and Strings
Daniel Freed, lecture 6 of Classical field theory and Supersymmetry, IAS/Park City Mathematics Series Volume 11 (2001) (pdf)
Daniel Freed, Lecture 3 of Five lectures on supersymmetry
Veeravalli Varadarajan, section 6,5 of Supersymmetry for mathematicians: An introduction, Courant lecture notes in mathematics, American Mathematical Society, Providence, R.I 2004 (pdf)
Antoine Van Proeyen, Tools for supersymmetry (arXiv:hep-th/9910030)
Last revised on July 19, 2020 at 13:43:23. See the history of this page for a list of all contributions to it.