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I'm a math grad student working on numerical procedures for the Dirac equation, and I'd like to be able to incorporate the neutral current interaction

neutrino + fermion -> Z bozon -> neutrino + fermion <- poorly impersonated Feynman diagram

into the Dirac equation as a potential term to allow me to calculate more physically meaningful results. The problem is, I'm familiar enough with the notation to expand the neutral current interaction into full matrix form so I can start programming it into the computer.

Here's the neutral current equation from Wikipedia's entry on Neutral Current

and here's the neutral current component of the Electroweak Lagrangian

Which of these is most appropriate to integrate into the Dirac equation, and how so?

How can I find the formal definition of each of the terms so I can expand them? (the gamma matrices are pretty straightforward, of course, but I have trouble with other terms like the matrix definition of weak isospin and the vector and axial vector couplings)

Any help would be appreciated, including links to papers on this topic.

Thanks!

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# How to incorporate the neutral current into the Dirac equation

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