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Qmechanic explained a way in which something with the word "commutator" in it doesn't vanish when applied to two of the same operator. However, I feel it is necessary to point out that plain commutators, as seen in a quantum mechanics course, really, honestly, always, and without fail satisfy $[Q,Q] = 0$ for any operator $Q$. This is because $[A,B]$ is ...


7

I) Yes, they are probably referring to that a Grassmann-odd operator needs not (super)commute with itself. Take e.g. the 1st order Grassmann-odd differential operator $$\tag{1} D~:=~\frac{d}{d\theta}+ \theta\frac{d}{dt}. $$ In eq. (1) $t$ is a Grassmann-even variable and $\theta$ is a Grassmann-odd variable, which (super)commute $$\tag{2} ...


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A theory with N=2 supersymmetry, where particles have two superpartners, has mirror symmetry built in. Nir Polonsky wrote some papers about an N=2 extension of the standard model (e.g.). The main problem for such a theory are the chiral Yukawa interactions between fermions and the Higgs field, which give fermions their mass in the SM. The mirror symmetry of ...


1

$R$ Parity is a discrete $Z_2 $ symmetry while an $R$ symmetry is a global continuous symmetry. If you use a $Z_2$ symmetry to build your model then each field can just be either odd and even, that's it. If you impose a continuous symmetry then there are an infinite number of possible choices of $R$ charges. From a model building perspective, a continuous ...


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For a superfield $S$, an infinitesimal supersymmetric transformation gives : $\delta_\epsilon S = -i(\epsilon\mathcal{Q}+\bar{\epsilon}\bar{\mathcal{Q}})S$ Here $\mathcal{Q}_a$ and ${ \mathcal{\bar Q}}^{\dot a}$ are differential operators applying on the superfield: $\mathcal{Q}_a = i \partial_a - (\sigma^\mu \bar \theta)_a \partial_\mu$, ${ ...


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Two-dimensional surfaces are the Feynman diagrams of string theory. In quantum field theory one sums over one dimensional objects in order to calculate quantities like scattering cross sections or decay rates. This is due to the fact that in this framework, particles are represented as zero dimensional objects, i.e. their world lines are points. In ...



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