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Classifying quarks and leptons using LCTs


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Hi everyone, I would like to ask for opinions/expertises on the relations between quarks, leptons and spin representation of linear canonical transformations (LCTs) as described in this link 

https://en.wikipedia.org/wiki/Linear_canonical_transformation#Relation_to_particle_physics

Please find below a picture describing this relation as taken from the link. My main questions are 

1- Are the statements in this link correct and compatible with mainstream particle physics ? (any contradiction?)

2-Could someone explain with more details how to deduce this classification? (if it is correct ?) 

 

Thank you in advance

QuarksandleptonsLCT-1.png

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