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!

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# From Feynman diagrams to potential

Tags:

Loading...

Similar Threads - Feynman diagrams potential | Date |
---|---|

I Confused about Feynman diagrams | Jul 16, 2017 |

I Feynman Diagram for Double Charm Baryon | Jul 7, 2017 |

I Feynman diagram of the Vector Boson Fusion | Jun 24, 2017 |

I Correct Feynman rules for one loop diagram? | Jun 5, 2017 |

A How does one find the Feynman diagrams? | May 16, 2017 |

**Physics Forums - The Fusion of Science and Community**