1. Relativistic Quantum Mechanics
Lecture 8
Books Recommended:
Lectures on Quantum Field Theory by Ashok Das
Advanced Quantum Mechanics by Schwabl
Relativistic Quantum Mechanics by Greiner
Quantum Field Theory by Mark Srednicki

2. Continuity Equation
Dirac Eq. in Hamiltonian
----(1)
Hermitian conjugate of this Eq. Is
-----(2)

3. Multiplying (1)by from left and (2) by from
Right, we get
-----(3)
Which is continuity eq

4. In (3), we write
(4)
Thus
---(5)
We write, current four vector
----(6)
So continuity eq become
(7)

5. Total probability density is constant

6. Dirac hole theory
Dirac equation has positive as well as negative
Energy solutions
Negative energy states may cause problem as there
May be transitions positive to negative states
and system may collapse.

7. Dirac particles are spin ½ particles and obey Pauli
exclusion principle.
Dirac assumed that all the negative energy states
are filled with negative energy electrons and
hence no transitions are possible to these states.
When sufficient energy is provided, negative
energy electron jumps to the positive energy
States and leave a positive energy hole in ground
state. Energy requires is,