chapter  2
16 Pages

Isotopic Spin And Strangeness

The starting point is the observation that the proton and neutron have masses very close to each other:

mn −mp mp

≃ 0.15 · 10−2 . (2.1)

Heisenberg interpreted this fact as a consequence of the invariance of the strong interaction Hamiltonian under transformations which change the states of the proton and neutron into arbitrary complex superpositions:(

p n

) → U

( p n

) (2.2)

where U is a unitary matrix, to preserve the normalisation |p|2 + |n|2. Every matrix of this type can be written as the product of a phase factor and a special matrix, i.e. a matrix with determinant equal to unity:

U = eiφUspec .