That's amazing. Damn I miss complex analysis. It's just not part of my current research.
Grassmann Variables are anti-commuting complex numbers
A Grassmann number can be understood as a 𝐧𝐨𝐧-𝐳𝐞𝐫𝐨 𝐬𝐪𝐮𝐚𝐫𝐞 𝐫𝐨𝐨𝐭 𝐨𝐟 𝐳𝐞𝐫𝐨
{A,B} = AB + BA is called an 𝐚𝐧𝐭𝐢-𝐜𝐨𝐦𝐦𝐮𝐭𝐚𝐭𝐨𝐫pic.twitter.com/bNsRwNHe0A
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What’s your research?
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The generators (Q) of supersymmetric transformations can be considered as "square roots" of spacetime translations (4-momentum P) since: {Q,Q-bar}~P with espectively: Grassmann: theta, theta-bar and x (spacetime) coordinates [x,x]=0, [x, theta]=0, {theta, theta}=0 etc. ([z,z}=0)
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Where superspace coordinates: z=(x, theta, theta-bar) are subject to the "graded commutator": [A,B}=AB-(-)^(ab)BA
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And these Grassmann numbers satisfy the "seesaw property": epsilon_(alpha, beta) theta^alpha theta^beta= theta^alpha theta_alpha = - theta_alpha theta^alpha i.e. a "minus-sign" since the 2-spinor indices are raised/lowered by the anti-symmetric epsilon.pic.twitter.com/UNoZnl2hgn
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Good introductory reads: (And do not forget Moshe Carmeli's accounts on two-spinors and relativity and: Subrahmanyan Chandrasekhar's "Mathematical Theory on Black Holes").pic.twitter.com/LpGNG4Xw5e
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Love the way that Grassmann numbers leads to the idea of holomorphic functions.
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Ok now do deformations. :)
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