Chapter V Interacting Fields Lecture 5 Books Recommended: Lectures on Quantum Field Theory by Ashok Das Advanced Quantum Mechanics by Schwabl

Quantum Electrodynamics (QED) Interaction Hamiltonian We use following normalized definition for One particle state

For fermions, If normaliztion condiiton is Then Fourier decomposition of field is However, if Then

Also, we have For photon field

One particle state for fermions For photon field

Consider Using anticommutator We get

Lines in Feynman Diagrams

Interaction Hamiltonian of QED, operators spitted in positive and negative frequency part Above Eq is sum of total 8 terms = e:( ):

Scattering Processes Examples S-matrix -----(1) First order QED process ---(2)

See slide (9) for all process described by (2). E.g. ---(3) Initial state -----(4) Final state ---(5)

From (2) we have ----(6)

----(7)

----(8) Using We have = ----(9)