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.
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.
Supercharge is described by the Super-Poincaré algebra.
Supercharge commutes with the Hamiltonian operator:
- [ Q , H ] = 0
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