Consider Weyl algebra, i.e. the algebra of $x^i$ and $p_i=\frac{\partial}{\partial x^i}$, its elements are differential operators $F(x,p)$. Weyl algebra is $\mathbb{Z}_2$ graded, hence one ask if there exists a supertrace. It turns out that there is one $$str\, F(x,p)=F(0,0)$$ I am looking for original references where this fact was established. Say, Pinczon et al in a 2005 paper "Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform" mention this fact without any refs.
Supertrace on Weyl algebra
John
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