Tuesday, 10 September 2019

special relativity - Heuristic derivation of Wmu=frac12epsilonmunusigmarhoPnuJsigmarho using combination of physical and mathematical arguments


If a simple systematic way to derive or guess (either mathematically or by a combination of physical arguments and mathematics) that one of the Casimir operator of Poincare group is W2WμWμ where Wμ=12ϵμνσρPνJσρ. In physics textbooks, (1) is given as a definition, and from which one can check that W2WμWμ is indeed a Casimir. But I find this definition of Wμ to be quite non-trivial to guess. So I'm not looking for a rigorous derivation and if there are physical arguments to achieve this, it will do for me.




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