- #1

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The term is Tr[[tex]\displaystyle{\not}p'\gamma^{\nu}\displaystyle{\not}k'\gamma^{\mu}\displaystyle{\not}k\gamma_{\nu}\displaystyle{\not}p\gamma_{\mu}[/tex]]

(here first two momenta are p' and k')

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- Thread starter karangovil
- Start date

- #1

- 1

- 0

The term is Tr[[tex]\displaystyle{\not}p'\gamma^{\nu}\displaystyle{\not}k'\gamma^{\mu}\displaystyle{\not}k\gamma_{\nu}\displaystyle{\not}p\gamma_{\mu}[/tex]]

(here first two momenta are p' and k')

- #2

- 25

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You can use some contraction identity (Peskin p. 805):

[tex]\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma^{\sigma}\gamma_{\mu}=

-2\gamma^{\sigma}\gamma^{\rho}\gamma^{\nu} [/tex]

[tex]\gamma^{\mu}\gamma^{\nu}\gamma^{\rho}\gamma_{\mu}=

4 g^{\nu \rho} [/tex].

Your term is:

[tex]Tr[ \gamma^{\delta}\gamma^{\nu}\gamma^{\alpha}\gamma^{\mu}\gamma^{\beta} \gamma_{\nu}\gamma^{\gamma}\gamma_{\mu}k'_{\alpha}k_{\beta}p_{\gamma}p'_{\delta}

]=-2Tr[ \gamma^{\delta}\gamma^{\beta}\gamma^{\mu}\gamma^{\alpha} \gamma^{\gamma}\gamma_{\mu}k'_{\alpha}k_{\beta}p_{\gamma}p'_{\delta}]

=[/tex]

[tex]=-8Tr[ \gamma^{\delta}\gamma^{\beta}k_{\beta}p'_{\delta}(k' \cdot p)

] =-32(k'\cdot p) (k\cdot p') [/tex]

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