isospin

Isospin, short for isotopic spin or isospin symmetry, is an internal quantum number used in the description of hadrons under the strong interaction. It was introduced by Werner Heisenberg in 1932 to explain the nearly identical strong interactions of protons and neutrons despite their electric charge difference. Isospin treats protons and neutrons as two states of a single particle, related by SU(2) rotations in flavor space.

Isospin is described by an SU(2) symmetry; the nucleon is an isospin doublet with total isospin I = 1/2. The third component, Iz, distinguishes protons and neutrons: Iz = +1/2 for proton and Iz = -1/2 for neutron. Pions form an isotriplet with I = 1: π+ has Iz = +1, π0 has Iz = 0, and π− has Iz = −1. It is important to note that isospin is not literal spin; it is an internal quantum number associated with flavor.

In terms of quarks, up and down quarks carry isospin I = 1/2 with Iz(up) = +1/2 and Iz(down) = −1/2. The strong interaction is approximately invariant under SU(2) rotations between up and down quarks; the symmetry is exact in the limit of equal up and down masses and negligible electromagnetic effects, and it is broken by quark mass differences and electromagnetism.

Isospin is conserved in strong interactions and relates amplitudes for different charge channels. It is embedded in the broader SU(3) flavor symmetry, where isospin is the SU(2) subgroup generated by the Pauli matrices; the concept remains a useful organizing principle in hadron spectroscopy and reaction analyses.