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Grassmann Variables Representation?

+ 5 like - 0 dislike
57 views

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.

This post imported from StackExchange Physics at 2014-04-05 17:32 (UCT), posted by SE-user Jaswin
asked Jun 1, 2012 in Theoretical Physics by Jaswin (105 points) [ no revision ]
Related: physics.stackexchange.com/q/95259

This post imported from StackExchange Physics at 2014-04-05 17:32 (UCT), posted by SE-user Christian LHC

1 Answer

+ 4 like - 0 dislike

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.

This post imported from StackExchange Physics at 2014-04-05 17:32 (UCT), posted by SE-user Kostya
answered Jun 1, 2012 by Kostya (310 points) [ no revision ]
This seems related to the Jordan-Wigner transformation that maps a fermion system to a boson system.

This post imported from StackExchange Physics at 2014-04-05 17:32 (UCT), posted by SE-user Xiao-Gang Wen

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