One approach to the representation theory of super Lie algebras is to restrict attention to representations in one space-time dimension and having ${\displaystyle N}$  supersymmetry generators, i.e., to ${\displaystyle (1|N)}$  superalgebras. In that case, the defining algebraic relationship among the supersymmetry generators reduces to

${\displaystyle \{Q_{I},Q_{J}\}=2i\delta _{IJ}\partial _{\tau }}$ .

Here ${\displaystyle \partial _{\tau }}$  denotes partial differentiation along the single space-time coordinate. One simple realization of the ${\displaystyle (1|1)}$  algebra consists of a single bosonic field ${\displaystyle \phi }$ , a fermionic field ${\displaystyle \psi }$ , and a generator ${\displaystyle Q}$  which acts as

${\displaystyle Q\phi =i\psi }$ ,

${\displaystyle Q\psi =\partial _{\tau }\phi }$ .

Since we have just one supersymmetry generator in this case, the superalgebra relation reduces to ${\displaystyle Q^{2}=i\partial _{\tau }}$ , which is clearly satisfied. We can represent this algebra graphically using one solid vertex, one hollow vertex, and a single colored edge connecting them.

• Feynman diagram

• http://golem.ph.utexas.edu/category/2007/08/adinkras.html
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• http://www.thegreatcourses.com/courses/superstring-theory-the-dna-of-reality.html