- #1
blankvin
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Homework Statement
I am working through an example in Chapter 6 of Quigg's Gauge Theories. I have it mostly figured out, with the exception of how to work out the [itex]S^{\mu}S^{\nu}[/itex] term. All he writes is "...the term is impotent between massless spinors."
Homework Equations
I begin with:
What I want to know is how to obtain the factors that include [itex]S[/itex]:
The Attempt at a Solution
I have all of the terms except those which include [itex]S[/itex]. An explicit calculation or explanation would be extremely appreciated!
[Edit] I will show my work to point out where I am stuck.
I worked out the term involving [itex]g^{\mu\nu}[/itex]. After the contraction of [itex]\gamma_\nu g^{\mu\nu}[/itex], the polarization vectors contract with the terms in square brackets to give:
[itex]\epsilon_+^{*\alpha}\epsilon_-^{*\beta}[...] = \epsilon_+^{*} \cdot \epsilon_-^{*} (k_- - k_+)_{\nu} + \epsilon_-^{*} \cdot k_+ \epsilon_{+\nu}^* - \epsilon_+^* \cdot k_- \epsilon_{-\nu}^* [/itex] [1]
My understanding is that the [itex]S^{\mu}S^{\nu}[/itex] will act on [1] above, but I do not see how to get the desired result. I thought that the contravariant [itex]S^{\nu}[/itex] term would contract with the covariants, but instead somehow the [itex]k_+[/itex] and [itex]k_-[/itex] in the second and third terms of [1] above are replaced by [itex]S[/itex]. Either this is something I do not quite get, or I am being foolish.blankvin
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