Nucleon Masses

The nucleon masses can be written in terms of irreducible representations of isospin. The effective hamiltonian that describes the nucleon masses is

$${\cal H}\ =\ M_p p^\dagger p\ +\ M_n n^\dagger n$$

$$\ =\ {1\over 2}\left( M_p+M_n\right) \left( p^\dagger p + n^\dagg... ...t) \ +\ {1\over 2}\left( M_p-M_n\right) \left( p^\dagger p - n^\dagger n\right)$$

$$\ =\ {1\over 2}\left( M_p+M_n\right) N^\dagger N \ +\ {1\over 2}\left( M_p-M_n\right) N^\dagger \tau^3 N \ \ \ .$$ (36)

The first term is called the ``isoscalar mass term'' (it transforms as a scalar under isospin transformations), and the second is called the ``isovector mass term'' (it transforms as a vector, $\tau^a$ under isospin transformations).