Supercharge Explained

In theoretical physics, a supercharge is a generator of supersymmetry transformations. It is an example of the general notion of a charge in physics.

Supercharge, denoted by the symbol Q, is an operator which transforms bosons into fermions, and vice versa. Since the supercharge operator changes a particle with spin one-half to a particle with spin one or zero, the supercharge itself is a spinor that carries one half unit of spin.^{[1] [2]}

Depending on the context, supercharges may also be called Grassmann variables or Grassmann directions; they are generators of the exterior algebra of anti-commuting numbers, the Grassmann numbers. All these various usages are essentially synonymous; they refer to the

Z _{2} grading between bosons and fermions, or equivalently, the grading between c-numbers and a-numbers. Calling it a charge emphasizes the notion of a symmetry at work.

Commutation

Supercharge is described by the super-Poincaré algebra.

Supercharge commutes with the Hamiltonian operator:

[Q, H ] = 0

So does its adjoint.

See also

• R-symmetry

References

1. Web site: Supersymmetry to the rescue? . The Official String Theory Web Site . dead . https://web.archive.org/web/20181102164833/http://www.superstringtheory.com/experm/exper4a.html . 2018-11-02.
2. Web site: von Hippel . Matthew . Supersymmetry, to the Rescue! . 4 Gravitons The trials and tribulations of four gravitons and a postdoc . 18 April 2021.