Question related to completeness relation for photons

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The discussion revolves around understanding the completeness relation for photons, specifically the term q^ and its significance. The user seeks clarification on how to solve an exercise from "Quarks and Leptons" by Halzen and Martin. There is a request for a definition of the term ελ and guidance on performing calculations related to it. Participants emphasize the importance of grasping these concepts for a deeper understanding of modern particle physics. Additional bibliographic resources are suggested to aid in further study.
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Question is posted below.
Relevant Equations
completeness relation
Hi
Would you explain to me what is the q^ and how they are related to completeness.How can i solve this exercise?It is from "Quarks and leptons An Introductory course in Modern Particle Physics" of Halzen and Alan D.Martin.Also, can you point me to a useful bibliography?

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Just write down the definition of the ##\epsilon_{\lambda}## and do the calculation by "brute force" (it's not too difficult).
 
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Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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