I met a problem when I read the textbook "Relativistic Quantum Mechanics" by J.D.Bjorken. He said we can get the potential(adsbygoogle = window.adsbygoogle || []).push({});

V(r_1,r_2)=[itex]\frac{f^{2}}{\mu^{2}}(1-P_{ex})(\tau_1\cdot\tau_2)(\sigma_1\cdot\nabla_1)(\sigma_2\cdot\nabla_1)\frac{e^{-\mu|r_1-r_{2}|}}{|r_1-r_{2}|}[/itex]

(10.51)

from the amplitude

[itex]S_{fi}=\frac{(-ig_0)^2M^2}{(2\pi)^2\sqrt{E_1E_2E'_1E'_2}}(2\pi)^4\delta^4(p_1+p_2-p'_1-p'_2){[\chi^{+}_1\bar{u}(p'_1)i\gamma^5\tau u(p_1)\chi_1]\frac{i}{(p'_1-p_1)^2-\mu^2}\cdot[\chi^{+}_2\bar{u}(p'_2)i\gamma^5\tau u(p_2)\chi_2]

-[\chi^{+}_2\bar{u}(p'_2)i\gamma^5\tau u(p_1)\chi_1]\frac{i}{(p'_2-p_1)^2-\mu^2}\cdot[\chi^{+}_1\bar{u}(p'_1)i\gamma^5\tau u(p_2)\chi_2]}[/itex]

(10.45)

I can get the formula 10.50

[itex] \bar{u}(p'_1,s_1)\gamma^5 u(p_1,s_1)=u^{+}(s'_1)\frac{\sigma\cdot(p_1-p'_1)}{2M}u(s_1)[/itex]

but I can't get the 10.51, please give me an idea or suggestion, or any information, thank you!

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# From Feynman diagrams to potential

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