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If $(E,g,w)$ is a vector space $E$ with a metric $g$ and a symplectic form $w$; then we can define the complex parts $(1,0)$ and $(0,1)$, so that the complex Clifford algebra is: $$e_1 . f_1 + f_1 . e_1= -2 g(e,f)$$ $$e_0 . f_0 + f_0 . e_0=-2 g(e,f)$$ $$e_1 .f_0 - f_0 . e_1= w(e,f)$$ with $e_1$ in the $(1,0)$ part and $e_0$ in the $(0,1)$ part. Could we define from this algebra (mixed between the Clifford algebra and the Heisenberg algebra) the Dirac operator?

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  • $\begingroup$ Is AntBalan a new user name, for a user who is not new? $\endgroup$
    – Ben McKay
    Commented Oct 2, 2018 at 13:22

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