A. Zee, Quantum Field Theory in a Nutshell · Problem II.3.2

Field Theory Redux

Physics — QFT

Problem

Work out how the six objects contained in the

(1, 0)

and

(0, 1)

transform under the Lorentz group. Recall from your course on electromagnetism how the electric and magnetic fields

\vec{E}

and

\vec{B}

transform. Conclude that the electromagnetic field in fact transforms as

(1, 0) \oplus (0, 1)

. Show that it is parity that once again forces us to use a reducible representation.