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

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

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

4. Also, we have
For photon field

5. One particle state for fermions
For photon field

6. Consider
Using anticommutator
We get

7. Lines in Feynman Diagrams

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

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

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

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

14. ----(7)

15. ----(8)
Using
We have =
----(9)