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John
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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, some general comments are also welcome. 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.

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.

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, some general comments are also welcome. 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.

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José Figueroa-O'Farrill
José Figueroa-O'Farrill
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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""Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform" mention this fact without any refs.

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.

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.

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John
John
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Supertrace on Weyl algebra

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.