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We know that SUSY generators commute with translation $$ [P_\mu,Q_\alpha]=0 $$ I have some questions:

  1. What is this equation physical meaning?

  2. Is it possible to make "SUSY-like" generators that do not commute with translation? $[P_\mu,Q_\alpha]\ne0$

  3. What are the consequences of such relation?

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