## Parity

It is useful to understand the effect of a parity inversion on a Dirac spinor. Again work with the Dirac equation and its parity inverted form in which and remains unchanged (the same for the vector potential).

Since commutes with itself but anticommutes with the , it works fine.

(We could multiply it by a phase factor if we want, but there is no point to it.)

Therefore, under a parity inversion operation

Since , the third and fourth components of the spinor change sign while the first two don't. Since we could have chosen , all we know is that components 3 and 4 have the opposite parity of components 1 and 2.

Jim Branson 2013-04-22