- #1
maverick280857
- 1,789
- 4
Hi,
In a calculation I am doing, I encounter terms of the form
[tex]\bar{u}^{s_1}(\boldsymbol{\vec{p}})\gamma^{\mu}{v}^{s_2}(\boldsymbol{\vec{q}})[/tex]
where [itex]u[/itex] and [itex]v[/itex] are the electron and positron spinors. Is there any recipe for simplifying this expression, using the spin sums or other identities? I am unable to figure anything out except if I break u and v into components and consider various cases depending on what [itex]s_1[/itex], [itex]s_2[/itex] and [itex]\mu[/itex] are...which is too tedious.
(I have to compute the product of this with [itex]A_{\mu}(x)[/itex])
Suggestions would be greatly appreciated.
Thanks in advance.
PS -- I am not looking at the amplitude squared, so I probably cannot use the trace methods directly..
In a calculation I am doing, I encounter terms of the form
[tex]\bar{u}^{s_1}(\boldsymbol{\vec{p}})\gamma^{\mu}{v}^{s_2}(\boldsymbol{\vec{q}})[/tex]
where [itex]u[/itex] and [itex]v[/itex] are the electron and positron spinors. Is there any recipe for simplifying this expression, using the spin sums or other identities? I am unable to figure anything out except if I break u and v into components and consider various cases depending on what [itex]s_1[/itex], [itex]s_2[/itex] and [itex]\mu[/itex] are...which is too tedious.
(I have to compute the product of this with [itex]A_{\mu}(x)[/itex])
Suggestions would be greatly appreciated.
Thanks in advance.
PS -- I am not looking at the amplitude squared, so I probably cannot use the trace methods directly..
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