Hey guys! A question:(adsbygoogle = window.adsbygoogle || []).push({});

My QFT Lagrangian, fournishes through Noether's thm plus relativistic invariance a supposedly unitary and a supposed representation of the Lorentz group. These are the operators meant to act on my Hilbert space of possible states.

What guarantees that this actually happens, ie: 1. The commutation relations of the lorentz algebra are actually satisfied, 2. The operators are hermitian (guarantiing a unitary representation). 3. They actually do what they are advertized to do ie: for example applying the z-direction angular momentum operator to a single particle state created by your creation operator does give what its suposed to. ie: the dirac field creates s=1/2, the scalar field s=0, etc..

i find it amazing and non trivial if conditions 1-3 are generally satisfied just because of lorentz invariance plus the right commutation relations for the fields! (if true for those two reasons alone then it might motivate the supposedly put in by hand commutations relations!)

maybe theres a good reference i could look at?

thanks!

simic

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# QFT and unitary Lorent representation

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