2 -? The photon propagator
We have used choice of a specific gauge transformaRon to modify the equaRon of moRon. The quesRon is how do you modify the Lagrangian to get this equaRon of
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17 déc. 2010 photon propagator in the Feynman gauge. For fermions different from e (or µ ?)
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fields and introduce the Feynman propagator and functional integral approach as a fermion processes in e+e? collisions tests of the gauge boson ...
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We have used choice of a specific gauge transformaRon to modify the equaRon of moRon The quesRon is how do you modify the Lagrangian to get this equaRon of
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Now consider photon propagators for different gauge conditions for the EM potential Consequently in the new gauge the Feynman propagator becomes
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with two vertices and one gauge boson propagator These are of order g2 On the other hand the last Feynman rule is a contribution to the amplitude in and
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The most common use of the propagator is in calculating probability amplitudes for particle interactions using Feynman diagrams. These calculations are usually carried out in momentum space.Is Feynman propagator symmetric?
It follows that the causal propagator ? ? ? + ? ? ? is skew-symmetric in its arguments: ? S ( x ? y ) = ? ? S ( y ? x ) .- Propagator is a model whose objective is to determine the position of satellite at any instance of time, with given acceleration and initial velocity.
Kinematics
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The notations in this appendix follow the book \An Introduction to Quantum FieldTheory" by M. Peskin and D. Schroeder.
Electroweak Feynman Rules in the Unitary Gauge (one fermionic generation)Propagators:W
ip 2m2W g ppm 2WZip 2m2Z g ppm 2z ip2g i(=p+m )p
2m2 (for any fermion )hi
p2m2HInitial and nal linesp
(p) incomingp (p) outgoingSummation over polarizations:
X polarizations (p)(p) =gfor photons X polarizations (p)(p) =g+ppm2for massive vectors
X spinsu(p)u(p) ==p+m;X spinsv(p)v(p) ==pm 1Vertices (all momenta are incoming):
Gauge boson self interactionsp
3A p 2W +p 1W igsinW((p1p2)g+ (p2p3)g+ (p3p1)g)p 3Z p 2W +p 1W igcosW((p1p2)g+ (p2p3)g+ (p3p1)g)W W +W W +ig2(2gggggg)Z
Z W W +ig2cos2W(2gggggg)A
A W W +ig2sin2W(2gggggg)Z
A W W +ig2cosWsinW(2gggggg)
2Higgs interactions
h hhi 32gm2Hm Wh eeigmeM Wh W +W igM Wgh Z Z i gMWcos 2Wghh hhi34 m 2Hm 2Whh W +W i g22 ghh Z Z i g22cos 2Wg 3
Fermion interactions with gauge bosons
W eig2 p2 (1 5)A +iQgsinWQis the fermion charge in units ofeZ
+ig2cosW (T3(15)2Qsin2W)T3= 1=2 for up quarks and neutrinos,
1=2 for down quarks and charged leptonsZ
ig4cosW (1 5) 4Some formulas for traces of gamma matrices
tr(1) = 4 tr(odd number of matrices) = 0 tr( ) = 4g tr( ) = 4(gggg+gg) tr(5) = 0
tr( 5 ) = 0 (proove it!) tr( 5 ) =4i =24 =6 =2() 5quotesdbs_dbs7.pdfusesText_5[PDF] ffl to ffl transfer
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