From Special Relativity to Feynman Diagrams.pdf

# F μν k and ρσ k define now the projector p k p k

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F μν ( k ) and ρσ ( k ). Define now the projector P ( k ) = ( P ( k ) μ ν ) : P ( k ) μ ν δ μ ν k μ k ν k 2 . (12.280) The reader can easily verify that P ( k ) n = P ( k ). From the general form ( 12.252 ) of the vacuum polarization tensor found in Sect.12.7 and the expression of D F μν ( k ) in ( 12.110 ), it follows that: i ρσ ( k ) D F σν ( k ) = − C ( k 2 ) P ( k ) ρ ν . (12.281) The corrected propagator in the chain approximation reads: D F = D F + D F [− i ] D F + D F [− i ] D F [− i ] D F + · · · = D F 1 i D F + ( i D F ) 2 + · · · = D F 1 C P + C 2 P + · · · = D F 1 P + n = 0 ( C ) n P = D F 1 P + 1 1 + C P , (12.282)

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• Fall '17
• Chris Odonovan

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