1. Chapter III
Dirac Field
Lecture 5
Books Recommended:
Lectures on Quantum Field Theory by Ashok
Das
Advanced Quantum Mechanics by Schwabl

2. Field Decomposition
+Ve and –Ve energy sol. Of Dirac Eq define
Complete basis i.e.,
----(1)
Above Eq satisfy
----(2)

3. We can invert Eq (1) and write
(3)
Used Massive
normalization

4. Similarly,
-(4)
Thus, from (3) and (4), we have
--(5)
---(6)

5. Anticommutation relation for the annihilation
and creation operators will be
------(7)

6. Hamiltonian

7. --(8)
Using,
-----(9)
Eq. (8) become.

9. (10)

10. For normal ordering
----(11)
Normal ordered Hamiltonian
----(12)

11. Action on vacuum
----(13)
One particle state created by action of
Creation operator on vacuum
----(14)