The positron spinor is actually just the same as the negative energy spinor when the momentum is reversed.

We name the **creation and annihilation operators for the positron states** to be
and
and identify them to be.

These

The Dirac field and Hamiltonian can now be **rewritten**.

All the

There is an (infinite) constant energy, similar but of opposite sign to the one for the quantized EM field,
which we must add to make the vacuum state have zero energy.
Note that, had we used commuting operators (Bose-Einstein) instead of anti-commuting, there would have been no
lowest energy ground state so this Energy subtraction would not have been possible.
**Fermi-Dirac statistics are required for particles satisfying the Dirac equation**.

Since the **operators creating fermion states anti-commute**,
fermion states must be antisymmetric under interchange.
Assume
and
are the creation and annihilation operators for fermions and that they anti-commute.

The

Its not hard to show that the

Note that the **spinors satisfy the following equations**.

Since we changed the sign of the momentum in our definition of , the momentum term in the Dirac equation had to change sign.

Jim Branson 2013-04-22