# The asymptotic behavior of the propagator of a field

In Steven Weinberg's book "The Quantum Theory of Fields" vol. I, Section 12.1, page 500, it writes:

"We will write the asymptotic behavior of the propagator $\Delta_f(k)$ of a field of type $f$ in the form

$$\Delta_f(k)\sim k^{-2+2s_f}$$

Looking back at Chapter 6, we see that $s_f=0$ for scalar fields, $s_f=\frac{1}{2}$ for Dirac fields, ans $s_f=1$ for massive vector fields. More generally, it can be shown that for massive fields of Lorentz transformation type $(A,B)$, we have $s_f=A+B$. Speaking loosely, we may call $s_f$ the 'spin'."

How can we show that $s_f=A+B$ holds for massive fields of type $(A,B)$? Does anyone have some ideas of the proof? Thanks a lot in advance!

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