# PlanetPhysics/Supersymmetry

*Supersymmetry* or Poincar\'e, (extended) quantum symmetry is usually defined as an extension of ordinary spacetime symmetries obtained by adjoining spinorial generators whose anticommutator yields a
translation generator: .

As further explained in ref. ^{[1]}:

"This

(super)symmetry...(of thesuperspace)... can be realized on ordinary fields (that are defined as certain functions of physical spacetime(s)) by transformations that mix bosons and fermions. \emph{Such realizations suffice to study supersymmetry (one can write invariant actions, etc.) but are as cumbersome and inconvenient as doing vector calculus component by component. A compact alternative to this `component field' approach is given by thesuperspace--superfieldapproach}", which is defined next.

*Quantum superspace, or superspacetimes* , can be defined as an extension(s) of ordinary spacetime(s) to include
additional anticommuting coordinates, for example, in the form of two-component Weyl spinors .

*(Quantum) superfields* are *functions* defined over such superspaces, or superspacetimes.
Taylor series expansions of the superfield functions can be then performed with respect to the anticommuting coordinates ; this Taylor series has only a finite number of terms and the series expansion
coefficients obtained in this manner are the ordinary `component fields' specified above.

**Remarks:**
Supersymmetry is expected to be manifested, or observable, in such superspaces, that is, the *supersymmetry algebras* are represented by translations and rotations involving *both* the spacetime and the anticommuting coordinates. Then, the transformations of the `component fields' can be computed from the Taylor expansion of
the *translated and rotated superfields* . Especially important are those transformations that mix boson
and fermion symmetries; further details are found in ref. ^{[2]}.

## All SourcesEdit

^{[1]}^{[2]}

## ReferencesEdit

- ↑
^{1.0}^{1.1}J.S. Gates, Jr, et al. "Superspace"., arxiv-hep-th/0108200 preprint (1983). - ↑
^{2.0}^{2.1}"Preprint of 1,001 Lessons in Supersymmetry." on line PDF.