Chapter V
Interacting Fields
Lecture 7
Books Recommended:
Lectures on Quantum Field Theory by Ashok
Das
 Advanced Quantum Mechanics by Schwabl
Feynman Diagrams and Rules for QED
In general S-matrix element takes the form
Amplitude is evaluated using the Feynman
diagrams.
Feynman Rules:
(i) Vertex point:
(ii) Internal Lines: (Propagator)
For photon
For Fermion
(iii) External lines
(incidence === annihilation)
(outgoing === creation)
(iv)
The spinor factors (γ matrices, SF propagators,
four-spinors) are ordered
for each fermion line such that reading them
from right to left amounts
to following the arrows along the fermion
lines
(v) For each closed fermion loop, multiply by
a factor (−1) and take the trace over the
spinor indices
(vi) At every vertex, the four-momenta of the
three lines that meet at this point satisfy
energy and momentum conservation.
(vii) It is necessary to integrate over all free
internal momenta (i.e., those not fixed by
four-momentum conservation)
Diagrams without loops are called tree level
diagrams.
Exercise: Draw the possible Feynman
diagrams and write expression for scattering
amplitudes using Feynman rules for
following QED scattering processes.
(i) e- + e+
(ii) e- + e+
(iii) e- + γ
e- + e+ (Bhabha scattering)
μ- + μ+
e- + γ (Compton scattering)
(iv) γ + γ
(v) e- + e-
e- + e- (pair production)
γ + γ (pair annihilation)