# How quantum field transforms in case of some particular spin

Except when a particle is spin-0, field of all particles transforms when frame of reference is changed, and this defines what spin is. The question is, specifically how does the quantum field transform in the corresponding equation, and how does this relate to the quantity of spin? I want to see how this works mathematically (specifically, I want to know spin-1/2 and spin-1, obviously.)

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Spin-1/2 fields transform as spinors, using the isomorphism $SL(2,C)\sim SO(3,1)$ in the case of 3+1 dimensions, and spin-1 fields transform as vectors (and the field strength as antisymmetric tensor). If you want to go beyond this, I think that you are asking about some basics of Lie groups which are 1) more mathematics than physics, 2) are covered in all basic introductions to QFT and sometimes already QM. –  Luboš Motl Oct 12 '12 at 12:24