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If I have a momentapand transform it via lorentz boost in x-direction with velocity v I'll get for the new 0th component_{μ}=(E,p_{x},p_{y},p_{z})E′=γE+γvpwhy is this in the limit of low velocities the same as transforming the energy by a galilei transformation with velocity_{x}v? Forγvpi get something like_{x}vpand with a galilei transformation I'll have terms (with_{x}+O(v³)p) like_{x}=mu1/2m(u−v)²=1/2mu²−vp. So in the relativistic case I got the wrong sing for_{x}+1/2mv²vpand lost the_{x}+O(v³)1/2mv²? Did I make a mistake?

Thanks for help

Neutrinos

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# Relativistic momentum (Lorentz boost) low velocity limit

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