Supercharge

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

For other uses, see Supercharge (disambiguation).

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]

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 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
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References
  1. Supersymmetry to the rescue?
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