A. Zee, Quantum Field Theory in a Nutshell · Problem VI.4.1
Field Theory Redux
Physics — QFT
Problem
Show that the vacuum expectation value of (σ,π) can indeed point in any direction without changing the physics. At first sight, this statement seems strange since, by virtue of its γ5 coupling to the nucleon, the pion is a pseudoscalar field and cannot have a vacuum expectation without breaking parity. But (σ,π) are just Greek letters. Show that by a suitable transformation of the nucleon field parity is conserved, as it should be in the strong interaction.