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/sci/ - Science & Math

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4304420 No.4304420 [Reply] [Original]

Why isn't there any contribution of the Fadeev-Popov ghosts to photon-photon scattering up to around second order?

How do the self-energy corrections in the photon propagator cancel?

>> No.4304452

Bump, I don't want to go on stackexchange and look like a babby.

Please /sci/?

>> No.4304462
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4304462

Why introduce ghosts in an abelian quantum field theory?

>> No.4304483

>>4304462
>implying i know

>> No.4304501
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4304501

>>4304483
you wouldn't do that.
anyway, regarding the order, you should just take a look at the feynman rules of the theory.
you want one gauge field in, one out, draw these two lines and look how you can connect them in a minimal way, infolving ghost propagators. then count the vertices, i.e. powers of the coupling and you see what order these graphs will contribute.

>> No.4304545
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4304545

Okay, I'll do the that step for you. This is not my field (no pun intended) but I think it might make sense. The relevant vertex is the bottom one in that pic. Since it's analogous to the QED vertex

http://upload.wikimedia.org/wikipedia/commons/thumb/6/66/QED_vertex.png/120px-QED_vertex.png

I assume you can compute polarization contributions of ghosts analogous to

http://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Vacuum_polarization.svg/500px-Vacuum_polari
zation.svg.png

notice how you put two of the g·f·\Gamma vertices from the pic together, which would be second order in g.

>> No.4304552
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4304552

g·f·p, apperently

>> No.4304713

Thanks guys, got it.

I really appreciate it.

>> No.4304724
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4304724

>>4304713
you should ask this kind of stuff on stack exchange though. It's not like there is the scientific elite there anyway and there are hardly any practical questions on QFT.

>> No.4305362

Not OP, but I figured this would be a good thread to post in.

What is a good intro text book for QFT assuming you have only covered a fair amount of QM?

What sort of maths are required?

>> No.4306229
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4306229

>>4305362
depending from your approaching angle, a good understanding of the Lagrangian formalism or field theor, especially Noether currents are of value. What is a fair amount of QM? People use Ryder, Peskin & Schröder or Weinberg if you're not afraid of math

>> No.4307111
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4307111

I asked and it yes, it really doesn't make sense for photons.