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hideelo
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I'm reading Weinberg's QFT volume 1. At the end of section 2.4 he is deriving the Inonu-Wigner contraction where he reduces the Poincaré group to the Euclidean one by taking the low velocity limit. In analyzing how the operators depend on velocity there are some I understand and some I don't.
I understand why W ~ mv^2, P ~ mv, M ~ m. I don't understand why J ~ 1, why isn't it on the same order as P? They both have linear velocity dependence. Also why is K ~ 1/v that means that for smaller velocity the effect gets bigger. I would expect that in the limit of small velocity, boosts just aren't a thing.
I understand why W ~ mv^2, P ~ mv, M ~ m. I don't understand why J ~ 1, why isn't it on the same order as P? They both have linear velocity dependence. Also why is K ~ 1/v that means that for smaller velocity the effect gets bigger. I would expect that in the limit of small velocity, boosts just aren't a thing.