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It might be a silly question, but I was never mathematically introduced to the topic. Is there a representation for Grassmann Variables using real field. For example, gamma matrices have a representation, is it not possible for Grassmann Variables? The reason for a representation is, then probably it will be easier to derive some of the properties.

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Related: – AltLHC Jan 29 '14 at 13:17
up vote 4 down vote accepted

I think that this Wikipedia article will tells this all.

The only problem is that for $n$ (I mean $\theta_1,\theta_2,...\theta_n$) Grassmann numbers you will need to use $2^n\times 2^n$ matrices.

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This seems related to the Jordan-Wigner transformation that maps a fermion system to a boson system. – Xiao-Gang Wen Jun 2 '12 at 4:51

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