Thursday, 16 November 2017

mathematical physics - Grassmann Variables Representation?


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.



Answer



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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