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

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

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

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

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

Hamiltonian

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

-------(10)

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

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