For a finite set of Grassmann variables $\theta_1, \theta_2,.. \theta_n$ one can form a matrix representation.
What about for a continuous Grassman variable $\theta(x)$ where $x$ are real numbers. Where $\theta(x)\theta(y)=-\theta(y)\theta(x)$. Is there a representation for these either in terms of matrices or calculus operators for example?
One would imagine that one could expand out a continuous Grassman variable in terms of an infinite set of Grassman variables $\theta(x)=\sum\limits_{n=0}^\infty \theta_n x^n$. Then the same question could be asked of an infinite set of Grassman variables.
Perhaps a representation could be found $\theta(x) = \theta(x)_{uv} = f(x,u,v)$ then:
$\int (f(x,u,v)f(y,v,w) + f(y,u,v)f(x,v,w)) dv=0$
Like matrices with continuous indices?