Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity.
Supergeometry is formulated in terms of -graded modules and sheaves over -graded commutative algebras (supercommutative algebras). In particular, superconnections are defined as Koszul connections on these modules and sheaves. However, supergeometry is not particular noncommutative geometry because of a different definition of a graded derivation.
Graded manifolds and supermanifolds also are phrased in terms of sheaves of graded commutative algebras. Graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces. There are different types of supermanifolds. These are smooth supermanifolds (-, -, -supermanifolds), -supermanifolds, and DeWitt supermanifolds. In particular, supervector bundles and principal superbundles are considered in the category of -supermanifolds. Definitions of principal superbundles and principal superconnections straightforwardly follow that of smooth principal bundles and principal connections. Principal graded bundles also are considered in the category of graded manifolds.
There is a different class of Quillen–Ne'eman superbundles and superconnections. These superconnections have been applied to computing the Chern character in K-theory, noncommutative geometry, and BRST formalism.
Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel...
algebra. Superalgebras also play an important role in related field of supergeometry where they enter into the definitions of graded manifolds, supermanifolds...
Supermetric is a mathematical concept used in a number of fields in physics. Supergeometry Supergravity Super Minkowski space Gauge gravitation theory Connor,...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
as a geometrical framework for understanding supersymmetry, in 1974; Supergeometry, the geometric basis for supersymmetry, in 1974; application of the...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
k) is the same as odd contact structure. Superspace Supersymmetry Supergeometry Graded manifold Batalin–Vilkovisky formalism Alice Rogers, Supermanifolds:...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
algebra), superschemes, supermetrics/supersymmetry, supermanifolds, supergeometry, and supergravity, namely in the context of superstring theory. "The...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...
quantum mechanics Supergravity Superstring theory Super vector space Supergeometry Supermathematics Superalgebra Lie superalgebra Super-Poincaré algebra...