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Spin is determined from the representation of the Lorentz group the quantum field transforms in. The projective finite-dimensional representations of the Lorentz group are labeled by two half-integers $(s_1,s_2)$. The spin of a field is the sum $s = s_1+s_2$. For example, a scalar transforms in $(0,0)$, a vector field in $(\frac{1}{2},\frac{1}{2})$, a Dirac ...


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How do we know that elementary particles possess definite parity? From the fitting of experimental data. Here is a review from 1965 , when we were still discovering the plethora of particles and started classifying them according to their quantum numbers. Since spin and parity are closely related quantities, there is usually some advantage in ...



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